Wikipedia:WikiProject Mathematics/PlanetMath Exchange/08-XX General algebraic systems

08A02 Relational systems, laws of composition

 * PM: closure of a relation, id=8492new! -- WP guess: closure of a relation -- Status:


 * PM: relational system, id=8788new! -- WP guess: relational system -- Status:

08A05 Structure theory

 * PM: direct product of algebras, id=8967new! -- WP guess: direct product of algebras -- Status:


 * PM: homomorphism between algebraic systems, id=7934new! -- WP guess: homomorphism between algebraic systems -- Status:


 * PM: isomorphism theorems on algebraic systems, id=8984new! -- WP guess: isomorphism theorems on algebraic systems -- Status:


 * PM: kernel of a homomorphism between algebraic systems, id=8593new! -- WP guess: kernel of a homomorphism between algebraic systems -- Status:


 * PM: Smarandache n-structure, id=5770new! -- WP guess: Smarandache n-structure -- Status:


 * PM: subalgebra of an algebraic system, id=8961new! -- WP guess: subalgebra of an algebraic system -- Status:


 * PM: subdirect product of algebraic systems, id=8972new! -- WP guess: subdirect product of algebraic systems -- Status:

08A30 Subalgebras, congruence relations

 * PM: congruence lattice, id=9407new! -- WP guess: congruence lattice -- Status:


 * PM: congruence relation on an algebraic system, id=8594new! -- WP guess: congruence relation on an algebraic system -- Status:


 * PM: ground fields and rings, id=7909new! -- WP guess: ground fields and rings -- Status:


 * PM: permutable congruences, id=9469new! -- WP guess: permutable congruences -- Status:


 * PM: simple algebraic system, id=9013new! -- WP guess: simple algebraic system -- Status:

08A40 Operations, polynomials, primal algebras

 * PM: coefficients of a polynomial, id=4953 -- WP: polynomial, coefficient -- Status: A
 * -- Paul August &#9742; 21:33, Feb 2, 2005 (UTC)


 * PM: polynomials in algebraic systems, id=9025new! -- WP guess: polynomials in algebraic systems -- Status:

08A99 Miscellaneous

 * PM: binary operation, id=3574 -- WP: binary operation -- Status: A
 * -- Paul August &#9742; 22:44, Feb 2, 2005 (UTC)


 * PM: filtered algebra, id=3938 -- WP: guess: filtered algebra -- Status: C
 * It certainly comes up in my work fairly often, so I think it should be covered. It could also be merged with the graded algebra article Jtwdog 17:36, 3 October 2005 (UTC)
 * Ok, I copied it and made some minor revisions. Jtwdog 16:51, 20 October 2005 (UTC)


 * PM: sum of ideals, id=6250 -- WP: ideal (ring theory) -- Status: A
 * Actually, it is covered. Jtwdog 17:36, 3 October 2005 (UTC)


 * PM: alternative definition of group, id=6876 -- Status: N
 * This is just a trivial fact that has no real significance. It appears to be an easy exercise from an algebra text. --Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: division in group, id=6877 -- Status: N
 * This is an article defining "division" in a group by $$x : y = xy^{-1}$$. There is also an elementary technical argument about groupoids.  None of this has encyclopedic noteworthiness.--Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: special notations in algebra, id=6955 -- WP guess: special notations in algebra -- Status:
 * This is an "index of notations" like you might find in the front of a book. I don't know if there's a need for this or not.  What do others think?--Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: biops, id=6385new! -- WP guess: biops -- Status:
 * This terminology doesn't appear to be in widespread use, as this page is the only mention of it that comes up on Google. (Could be a transliteration from some other language where the English word is different, though.) --Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: example of straight-line program, id=8382new! -- WP guess: example of straight-line program -- Status:


 * PM: inverse of inverse in a group, id=7676new! -- Status: N
 * This is just a proof that $$(a^{-1})^{-1} = a$$ in a group. Adequately covered in group. --Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: method of repeated squaring, id=8381new! -- WP: Exponentiation by squaring -- Status: A
 * Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: opposite group, id=9477new! -- WP guess: opposite group -- Status: NC
 * This article covers the categorical dual of a group, which is already defined and covered in Natural transformation. However it doesn't seem reasonable to force a beginning algebra student to learn category theory in order to learn what an opposite group is.  For that matter, we need an opposite functor article as well, and several of the examples on functor could stand to have their own pages.  Then it all needs linking together!  I'll try to work on this a little. --Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: quandles, id=8926new! -- WP guess: quandles -- Status: A
 * Dan131m (talk) 04:04, 4 October 2009 (UTC)


 * PM: straight-line program, id=8377new! -- WP guess: straight-line program -- Status:


 * PM: word, id=8137new! -- WP: word (group theory) -- Status: A
 * Dan131m (talk) 04:04, 4 October 2009 (UTC)

08B20 Free algebras

 * PM: algebraic categories without free objects, id=9104new! -- WP guess: algebraic categories without free objects -- Status:


 * PM: free algebra, id=9097new! -- WP guess: free algebra -- Status:


 * PM: free associative algebra, id=9098new! -- WP guess: free associative algebra -- Status:


 * PM: free commutative algebra, id=9103new! -- WP guess: free commutative algebra -- Status:


 * PM: free Lie algebra, id=9099new! -- WP guess: free Lie algebra -- Status:


 * PM: presentations of algebraic objects, id=9105new! -- WP guess: presentations of algebraic objects -- Status:

08B25 Products, amalgamated products, and other kinds of limits and colimits

 * PM: direct limit of algebraic systems, id=9156new! -- WP guess: direct limit of algebraic systems -- Status:


 * PM: reduced direct product, id=9482new! -- WP guess: reduced direct product -- Status:


 * PM: restricted direct product of algebraic systems, id=9395new! -- WP guess: restricted direct product of algebraic systems -- Status:

08B30 Injectives, projectives

 * PM: complex projective line, id=4818 -- WP: complex projective line -- Status: A
 * This article is extremely misclassified, but I suppose that's not very important to us. Jtwdog 17:38, 3 October 2005 (UTC)

08B99 Miscellaneous

 * PM: identity in a class, id=9035new! -- WP guess: identity in a class -- Status:

08C99 Miscellaneous

 * PM: Variation, id=6579 -- WP: Proportionality (mathematics) -- Status: A
 * -- Oddly named PM article, seems to really be about porportionality. Paul August &#9742; 04:45, Feb 3, 2005 (UTC)