Wikipedia:WikiProject Mathematics/PlanetMath Exchange/16-XX Associative rings and algebras

16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

 * PM: direct product of modules, id=1357 -- WP: direct product of modules -- Status: A
 * Oleg Alexandrov (talk) 23:46, 13 January 2007 (UTC)


 * PM: direct sum, id=1360 -- WP: direct sum -- Status: A
 * Oleg Alexandrov (talk) 23:46, 13 January 2007 (UTC)


 * PM: exact sequence, id=1354 -- WP: exact sequence -- Status: A
 * Oleg Alexandrov (talk) 23:46, 13 January 2007 (UTC)


 * PM: Noether normalization lemma, id=5688 -- WP: Noether normalization lemma -- Status: A
 * Oleg Alexandrov (talk) 23:46, 13 January 2007 (UTC)


 * PM: quotient ring, id=470 -- WP: quotient ring -- Status: A
 * Oleg Alexandrov (talk) 23:46, 13 January 2007 (UTC)


 * PM: left and right unity of ring, id=6936 -- WP: left and right unity of ring -- Status: A
 * Oleg Alexandrov (talk) 23:46, 13 January 2007 (UTC)


 * PM: commutant, id=9725new! -- WP guess: commutant -- Status:


 * PM: dual module, id=8037new! -- WP guess: dual module -- Status:


 * PM: inverses in rings, id=9457new! -- WP guess: inverses in rings -- Status:

16-01 Instructional exposition (textbooks, tutorial papers, etc.)

 * PM: order (of a ring), id=9488new! -- WP guess: order (of a ring) -- Status:

16B50 Category-theoretic methods and results

 * PM: counterexamples for products and coproduct, id=7872new! -- WP guess: counterexamples for products and coproduct -- Status:

16B70 Applications of logic

 * PM: additive inverse of a sum in a ring, id=7703new! -- WP guess: additive inverse of a sum in a ring -- Status:


 * PM: additive inverse of an inverse element, id=7708new! -- WP guess: additive inverse of an inverse element -- Status:


 * PM: additive inverse of the zero in a ring, id=7707new! -- WP guess: additive inverse of the zero in a ring -- Status:

16B99 Miscellaneous

 * PM: opposite ring, id=416 -- WP guess: opposite ring -- Status:


 * PM: unit, id=676 -- WP guess: unit -- Status:


 * PM: Klein 4-ring, id=6720 -- WP guess: Klein 4-ring -- Status:


 * PM: non-commutative rings of order four, id=9467new! -- WP guess: non-commutative rings of order four -- Status:

16D10 General module theory

 * PM: annihilator, id=996 -- WP guess: annihilator -- Status:


 * PM: annihilator is an ideal, id=3167 -- WP guess: annihilator is an ideal -- Status:


 * PM: artinian, id=2566 -- WP guess: artinian -- Status:


 * PM: composition series, id=5428 -- WP guess: composition series -- Status:


 * PM: conjugate module, id=377 -- WP guess: conjugate module -- Status:


 * PM: direct summand, id=6536 -- WP guess: direct summand -- Status:


 * PM: finitely generated module, id=4957 -- WP guess: finitely generated module -- Status:


 * PM: modular law, id=3173 -- WP guess: modular law -- Status:


 * PM: module, id=1022 -- WP guess: module -- Status:


 * PM: proof of modular law, id=3174 -- WP guess: proof of modular law -- Status:


 * PM: quotient module, id=4966 -- WP : quotient module -- Status: A
 * Oleg Alexandrov 05:03, 28 May 2005 (UTC)


 * PM: zero module, id=1005 -- WP guess: zero module -- Status:

16D20 Bimodules

 * PM: bimodule, id=987 -- WP guess: bimodule -- Status:

16D25 Ideals

 * PM: associated prime, id=1001 -- WP guess: associated prime -- Status:


 * PM: ideal generated by a subset of a ring, id=6242 -- WP guess: ideal generated by a subset of a ring -- Status:


 * PM: nilpotent ideal, id=994 -- WP guess: nilpotent ideal -- Status:


 * PM: primitive ideal, id=1007 -- WP guess: primitive ideal -- Status:


 * PM: product of ideals, id=411 -- WP guess: product of ideals -- Status:


 * PM: proper ideal, id=415 -- WP guess: proper ideal -- Status:


 * PM: semiprime ideal, id=990 -- WP guess: semiprime ideal -- Status:


 * PM: zero ideal, id=412 -- WP guess: zero ideal -- Status:


 * PM: Large ideal, id=7549 -- WP guess: Large ideal -- Status:


 * PM: dense ideals/subsets of a ring, id=8491new! -- WP guess: dense ideals/subsets of a ring -- Status:


 * PM: equivalence for semiprime rings, id=9739new! -- WP guess: equivalence for semiprime rings -- Status:


 * PM: ideal multiplication laws, id=7711new! -- WP guess: ideal multiplication laws -- Status:


 * PM: pairwise comaximal ideals property, id=9149new! -- WP guess: pairwise comaximal ideals property -- Status:

16D40 Free, projective, and flat modules and ideals

 * PM: absolutely flat, id=6166 -- WP guess: absolutely flat -- Status:


 * PM: faithfully flat, id=6167 -- WP guess: faithfully flat -- Status:


 * PM: finitely generated projective module, id=4068 -- WP guess: finitely generated projective module -- Status:


 * PM: flat module, id=1369 -- WP guess: flat module -- Status:


 * PM: free module, id=1381 -- WP guess: free module -- Status:


 * PM: free module, id=5420 -- WP guess: free module -- Status:


 * PM: projective cover, id=1380 -- WP guess: projective cover -- Status:


 * PM: projective module, id=1365 -- WP guess: projective module -- Status:

16D50 Injective modules, self-injective rings

 * PM: injective hull, id=1378 -- WP guess: injective hull -- Status:


 * PM: injective module, id=1083 -- WP guess: injective module -- Status:

16D60 Simple and semisimple modules, primitive rings and ideals

 * PM: central simple algebra, id=363 -- WP guess: central simple algebra -- Status:


 * PM: completely reducible, id=3873 -- WP guess: completely reducible -- Status:


 * PM: semisimple ring, id=5784 -- WP guess: semisimple ring -- Status:


 * PM: simple ring, id=414 -- WP guess: simple ring -- Status:


 * PM: example of reducible and irreducible G-modules, id=8831new! -- WP guess: example of reducible and irreducible G-modules -- Status:

16D70 Structure and classification, direct sum decomposition, cancellation

 * PM: subdirect product, id=5786 -- WP guess: subdirect product -- Status:


 * PM: subdirectly irreducible ring, id=5787 -- WP guess: subdirectly irreducible ring -- Status:


 * PM: Wedderburn-Artin theorem, id=5785 -- WP guess: Wedderburn-Artin theorem -- Status:


 * PM: Krull-Schmidt theorem, id=7238 -- WP guess: Krull-Schmidt theorem -- Status:

16D80 Other classes of modules and ideals

 * PM: essential submodule, id=1374 -- WP guess: essential submodule -- Status:


 * PM: faithful module, id=999 -- WP guess: faithful module -- Status:


 * PM: hereditary ring, id=6473 -- WP guess: hereditary ring -- Status:


 * PM: minimal prime ideal, id=989 -- WP guess: minimal prime ideal -- Status:


 * PM: module of finite rank, id=1106 -- WP guess: module of finite rank -- Status:


 * PM: semihereditary ring, id=6475 -- WP guess: semihereditary ring -- Status:


 * PM: simple module, id=1003 -- WP guess: simple module -- Status:


 * PM: superfluous submodule, id=1377 -- WP guess: superfluous submodule -- Status:


 * PM: uniform module, id=418 -- WP guess: uniform module -- Status:

16D90 Module categories ; module theory in a category-theoretic context; Morita equivalence and duality

 * PM: Morita equivalence, id=8851new! -- WP guess: Morita equivalence -- Status:

16D99 Miscellaneous

 * PM: hopfian module, id=5810 -- WP guess: hopfian module -- Status:


 * PM: socle, id=5837 -- WP guess: socle -- Status:

16E05 Syzygies, resolutions, complexes

 * PM: n-chain, id=4478 -- WP guess: n-chain -- Status:


 * PM: chain complex, id=1353 -- WP guess: chain complex -- Status:


 * PM: flat resolution, id=1372 -- WP guess: flat resolution -- Status:


 * PM: free resolution, id=1370 -- WP guess: free resolution -- Status:


 * PM: injective resolution, id=1373 -- WP guess: injective resolution -- Status:


 * PM: projective resolution, id=1371 -- WP guess: projective resolution -- Status:


 * PM: short exact sequence, id=1355 -- WP guess: short exact sequence -- Status:


 * PM: split short exact sequence, id=1356 -- WP guess: split short exact sequence -- Status:


 * PM: more on short exact sequences, id=6965 -- WP guess: more on short exact sequences -- Status:


 * PM: construction of an injective resolution, id=9500new! -- WP guess: construction of an injective resolution -- Status:


 * PM: tensor product of chain complexes, id=8321new! -- WP guess: tensor product of chain complexes -- Status:

16E10 Homological dimension

 * PM: projective equivalence, id=6505 -- WP guess: projective equivalence -- Status:

16E45 Differential graded algebras and applications

 * PM: differential graded algebra, id=7488 -- WP guess: differential graded algebra -- Status:

16E50 von Neumann regular rings and generalizations

 * PM: nested ideals in von Neumann regular ring, id=6463 -- WP guess: von Neumann regular ring -- Status:


 * PM: von Neumann regular, id=3295 -- WP guess: von Neumann regular ring -- Status:

16K40 Infinite-dimensional and general

 * PM: dense ring of linear transformations, id=7578 -- WP guess: dense ring of linear transformations -- Status:

16K50 Brauer groups

 * PM: Brauer group, id=372 -- WP guess: Brauer group -- Status:

16K99 Miscellaneous

 * PM: division ring, id=356 -- WP guess: division ring -- Status:


 * PM: division algebra, id=9117new! -- WP guess: division algebra -- Status:

16N20 Jacobson radical, quasimultiplication

 * PM: a ring modulo its Jacobson radical is semiprimitive, id=3149 -- WP guess: a ring modulo its Jacobson radical is semiprimitive -- Status:


 * PM: examples of semiprimitive rings, id=3172 -- WP guess: examples of semiprimitive rings -- Status:


 * PM: Jacobson radical, id=2856 -- WP guess: Jacobson radical -- Status:


 * PM: proof of characterizations of the Jacobson radical, id=3137 -- WP guess: proof of characterizations of the Jacobson radical -- Status:


 * PM: properties of the Jacobson radical, id=3152 -- WP guess: properties of the Jacobson radical -- Status:


 * PM: quasi-regularity, id=3681 -- WP guess: quasi-regularity -- Status:


 * PM: semiprimitive ring, id=2857 -- WP guess: semiprimitive ring -- Status:

16N40 Nil and nilpotent radicals, sets, ideals, rings

 * PM: Koethe conjecture, id=3691 -- WP guess: Koethe conjecture -- Status:


 * PM: nil and nilpotent ideals, id=3690 -- WP guess: nil and nilpotent ideals -- Status:


 * PM: nil is a radical property, id=5651 -- WP guess: nil is a radical property -- Status:


 * PM: nilpotency is not a radical property, id=5652 -- WP guess: nilpotency is not a radical property -- Status:


 * PM: properties of nil and nilpotent ideals, id=5650 -- WP guess: properties of nil and nilpotent ideals -- Status:


 * PM: upper nilradical, id=9872new! -- WP guess: upper nilradical -- Status:

16N60 Prime and semiprime rings

 * PM: prime ring, id=413 -- WP guess: prime ring -- Status:


 * PM: reduced ring, id=5762 -- WP guess: reduced ring -- Status:

16N80 General radicals and rings

 * PM: prime radical, id=995 -- WP guess: prime radical -- Status:


 * PM: radical theory, id=3682 -- WP guess: radical theory -- Status:

16P20 Artinian rings and modules

 * PM: Hopkins theorem, id=8119new! -- WP guess: Hopkins theorem -- Status:

16P40 Noetherian rings and modules

 * PM: example of right noetherian ring that is not left noetherian, id=5721 -- WP guess: example of right noetherian ring that is not left noetherian -- Status:


 * PM: noetherian, id=2575 -- WP guess: noetherian -- Status:


 * PM: noetherian ring, id=187 -- WP guess: noetherian ring -- Status:

16P60 Chain conditions on annihilators and summands: Goldie-type conditions, Krull dimension

 * PM: Goldie ring, id=5427 -- WP guess: Goldie ring -- Status:


 * PM: Goldie's theorem, id=5429 -- WP guess: Goldie's theorem -- Status:


 * PM: uniform dimension, id=5401 -- WP guess: uniform dimension -- Status:

16P99 Miscellaneous

 * PM: IBN, id=6537 -- WP guess: IBN -- Status:


 * PM: stably finite, id=5767 -- WP guess: stably finite -- Status:

16R10 $T$-ideals, identities, varieties of rings and algebras

 * PM: polynomial identity algebra, id=5816 -- WP guess: polynomial identity algebra -- Status:


 * PM: standard identity, id=5830 -- WP guess: standard identity -- Status:


 * PM: T-ideal, id=5831 -- WP guess: T-ideal -- Status:

16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)

 * PM: Ore domain, id=417 -- WP guess: Ore domain -- Status:

16S20 Centralizing and normalizing extensions

 * PM: ring of endomorphisms, id=5432 -- WP guess: ring of endomorphisms -- Status:

16S30 Universal enveloping algebras of Lie algebras

 * PM: Friedrichs' theorem, id=9101new! -- WP guess: Friedrichs' theorem -- Status:


 * PM: Lie element, id=9100new! -- WP guess: Lie element -- Status:

16S32 Rings of differential operators

 * PM: Weyl algebra, id=7305 -- WP guess: Weyl algebra -- Status:

16S34 Group rings, Laurent polynomial rings

 * PM: group ring, id=1595 -- WP guess: group ring -- Status:


 * PM: orthogonal idempotents of the group ring, id=5646 -- WP guess: orthogonal idempotents of the group ring -- Status:


 * PM: support, id=5400 -- WP guess: support -- Status:

16S36 Ordinary and skew polynomial rings and semigroup rings

 * PM: Gaussian polynomials, id=378 -- WP guess: Gaussian polynomials -- Status:


 * PM: q skew derivation, id=375 -- WP guess: q skew derivation -- Status:


 * PM: q skew polynomial ring, id=376 -- WP guess: q skew polynomial ring -- Status:


 * PM: sigma derivation, id=72 -- WP guess: sigma derivation -- Status:


 * PM: delta constant sigma, id=374 -- WP guess: delta constant sigma -- Status:


 * PM: skew derivation, id=369 -- WP guess: skew derivation -- Status:


 * PM: skew polynomial ring, id=373 -- WP guess: skew polynomial ring -- Status:

16S50 Endomorphism rings; matrix rings

 * PM: generalized matrix ring, id=6245 -- WP guess: generalized matrix ring -- Status:


 * PM: matrix ring, id=7908new! -- WP guess: matrix ring -- Status:

16S90 Maximal ring of quotients, torsion theories, radicals on module categories

 * PM: classical ring of quotients, id=5402 -- WP guess: classical ring of quotients -- Status:

16S99 Miscellaneous

 * PM: Peirce decomposition, id=6246 -- WP guess: Peirce decomposition -- Status:


 * PM: corner of a ring, id=7682new! -- WP guess: corner of a ring -- Status:

16U10 Integral domains

 * PM: Prüfer domain, id=4507 -- WP guess: Prüfer domain -- Status:

16U20 Ore rings, multiplicative sets, Ore localization

 * PM: Ore condition, id=5403 -- WP guess: Ore condition -- Status:


 * PM: Ore's theorem, id=5404 -- WP guess: Ore's theorem -- Status:


 * PM: saturated, id=2737 -- WP guess: saturated -- Status:

16U70 Center, normalizer (invariant elements)

 * PM: center (rings), id=3065 -- WP guess: center (rings) -- Status:

16U99 Miscellaneous

 * PM: anti-idempotent, id=4501 -- WP guess: anti-idempotent -- Status:


 * PM: Dedekind-finite, id=5766 -- WP guess: Dedekind-finite -- Status:


 * PM: idempotent, id=3558 -- WP guess: idempotent -- Status:


 * PM: Baer ring, id=7864new! -- WP guess: Baer ring -- Status:


 * PM: idempotent classifications, id=9046new! -- WP guess: idempotent classifications -- Status:

16W10 Rings with involution; Lie, Jordan and other nonassociative structures

 * PM: involutary ring, id=7625 -- WP guess: involutary ring -- Status:

16W22 Actions of groups and semigroups; invariant theory

 * PM: group action, id=1516 -- WP guess: group action -- Status:


 * PM: stabilizer, id=1518 -- WP guess: stabilizer -- Status:


 * PM: faithful group action, id=5259 -- WP guess: faithful group action -- Status:

16W30 Coalgebras, bialgebras, Hopf algebras ; rings, modules, etc. on which these act

 * PM: almost cocommutative bialgebra, id=4123 -- WP guess: almost cocommutative bialgebra -- Status:


 * PM: bialgebra, id=3523 -- WP guess: bialgebra -- Status:


 * PM: coalgebra, id=3522 -- WP guess: coalgebra -- Status:


 * PM: coinvariant, id=4729 -- WP guess: coinvariant -- Status:


 * PM: comodule, id=3999 -- WP guess: comodule -- Status:


 * PM: comodule algebra, id=4005 -- WP guess: comodule algebra -- Status:


 * PM: comodule coalgebra, id=4007 -- WP guess: comodule coalgebra -- Status:


 * PM: Hopf algebra, id=3524 -- WP guess: Hopf algebra -- Status:


 * PM: module algebra, id=4004 -- WP guess: module algebra -- Status:


 * PM: module coalgebra, id=4006 -- WP guess: module coalgebra -- Status:


 * PM: the dual of a coalgebra is an algebra, id=8762new! -- WP guess: the dual of a coalgebra is an algebra -- Status:


 * PM: Faà di Bruno's formula, id=8853new! -- WP guess: Faà di Bruno's formula -- Status:

16W50 Graded rings and modules

 * PM: graded algebra, id=3071 -- WP guess: graded algebra -- Status:


 * PM: graded module, id=193 -- WP guess: graded module -- Status:


 * PM: supercommutative, id=3973 -- WP guess: supercommutative -- Status:

16W55 ``Super (or ``skew) structure

 * PM: graded tensor product, id=3070 -- WP guess: graded tensor product -- Status:


 * PM: superalgebra, id=3082 -- WP guess: superalgebra -- Status:


 * PM: supernumber, id=3463 -- WP guess: supernumber -- Status:

16W99 Miscellaneous

 * PM: Hamiltonian quaternions, id=2846 -- WP guess: Hamiltonian quaternions -- Status:


 * PM: Hamiltonians versus the complex numbers, id=8076new! -- WP guess: Hamiltonians versus the complex numbers -- Status:

16Y30 Near-rings

 * PM: near-ring, id=3968 -- WP guess: near-ring -- Status:

16Y60 Semirings

 * PM: semiring, id=2617 -- WP guess: semiring -- Status:


 * PM: idempotent semiring, id=7866new! -- WP guess: idempotent semiring -- Status: