Wikipedia:WikiProject Mathematics/PlanetMath Exchange/06-XX Order, lattices, ordered algebraic structures

06-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

 * PM: equivalence relation, id=349 -- WP: equivalence relation -- Status: A
 * AdamSmithee 14:17, 3 January 2006 (UTC)

06A05 Total order

 * PM: characterization of ordered groups of rank one, id=6607 -- WP guess: characterization of ordered groups of rank one -- Status:


 * PM: corollaries of basic theorem on ordered groups, id=6606 -- WP guess: corollaries of basic theorem on ordered groups -- Status:


 * PM: isolated subgroup, id=6605 -- WP guess: isolated subgroup -- Status:


 * PM: lowest upper bound, id=452 -- WP: supremum -- Status: A
 * Paul August &#9742; 22:52, September 2, 2005 (UTC)


 * PM: ordered group, id=6595 -- WP guess: ordered group -- Status:


 * PM: proof of basic theorem about ordered groups, id=6598 -- WP guess: proof of basic theorem about ordered groups -- Status:


 * PM: proof of embedding theorem for ordered abelian groups of rank one, id=6614 -- WP guess: proof of embedding theorem for ordered abelian groups of rank one -- Status:


 * PM: total order, id=124 -- WP: total order -- Status: A
 * Paul August &#9742; 03:50, 9 May 2006 (UTC)


 * PM: properties of well-ordered sets, id=7231 -- WP guess: properties of well-ordered sets -- Status:


 * PM: dense total order, id=8888new! -- WP guess: dense total order -- Status:


 * PM: supremum over closure, id=9446new! -- WP guess: supremum over closure -- Status:

06A06 Partial order, general

 * PM: directed set, id=3249 -- WP: directed set -- Status: NM
 * AdamSmithee 09:39, 9 January 2006 (UTC)


 * PM: infimum, id=339 -- WP: infimum -- Status: A
 * AdamSmithee 14:26, 3 January 2006 (UTC)


 * PM: sets that do not have an infimum, id=3607 -- WP: infimum -- Status: NM
 * AdamSmithee 14:26, 3 January 2006 (UTC)


 * PM: supremum, id=340 -- WP: supremum -- Status: A
 * AdamSmithee 14:26, 3 January 2006 (UTC)


 * PM: upper bound, id=450 -- WP: upper bound -- Status: A
 * AdamSmithee 14:26, 3 January 2006 (UTC)


 * PM: atom, id=7153 -- WP guess: atom -- Status:


 * PM: dual of Dilworth's theorem, id=6740 -- WP guess: dual of Dilworth's theorem -- Status:


 * PM: poset height and width, id=6739 -- WP guess: poset height and width -- Status:


 * PM: arbitrary join, id=9848new! -- WP guess: arbitrary join -- Status:


 * PM: chain finite, id=9180new! -- WP guess: chain finite -- Status:


 * PM: Dilworth's theorem, id=7794new! -- WP guess: Dilworth's theorem -- Status:


 * PM: dimension of a poset, id=8744new! -- WP guess: dimension of a poset -- Status:


 * PM: eventual property, id=8770new! -- WP guess: eventual property -- Status:


 * PM: extension of a poset, id=8713new! -- WP guess: extension of a poset -- Status:


 * PM: fence, id=9439new! -- WP guess: fence -- Status:


 * PM: height of an element in a poset, id=8705new! -- WP guess: height of an element in a poset -- Status:


 * PM: ideal completion of a poset, id=9340new! -- WP guess: ideal completion of a poset -- Status:


 * PM: lattice interval, id=7701new! -- WP guess: lattice interval -- Status:


 * PM: order ideal, id=9305new! -- WP guess: order ideal -- Status:


 * PM: orders in a number field, id=9132new! -- WP guess: orders in a number field -- Status:


 * PM: product of posets, id=8743new! -- WP guess: product of posets -- Status:


 * PM: pure poset, id=9682new! -- WP guess: pure poset -- Status:


 * PM: rank-selected poset, id=8541new! -- WP guess: rank-selected poset -- Status:


 * PM: upper set, id=7801new! -- WP guess: upper set -- Status:


 * PM: upper set operation is a closure operator, id=8908new! -- WP guess: upper set operation is a closure operator -- Status:

06A07 Combinatorics of partially ordered sets

 * PM: Eulerian poset, id=5552 -- WP guess: Eulerian poset -- Status:


 * PM: well quasi ordering, id=4653 -- WP guess: well quasi ordering -- Status:


 * PM: \mathbf{ab}-index of graded posets, id=7737new! -- WP guess: \mathbfab-index of graded posets -- Status:


 * PM: connected poset, id=9449new! -- WP guess: connected poset -- Status:

06A11 Algebraic aspects of posets

 * PM: Newtonian coalgebra, id=9044new! -- WP guess: Newtonian coalgebra -- Status:

06A12 Semilattices

 * PM: a semilattice is a commutative band, id=3320 -- WP: semilattice -- Status: A
 * AdamSmithee 10:03, 9 January 2006 (UTC)


 * PM: semilattice, id=3317 -- WP: semilattice -- Status: NM
 * i.e. spell out in the intro (obvious) remarks that a join semilattice is dual to a meet sl + semilattice that is both join and meet = lattice AdamSmithee 10:03, 9 January 2006 (UTC)


 * PM: join, id=2611 -- WP: Lattice (order) -- Status: A
 * Paul August &#9742; 03:54, 9 May 2006 (UTC)


 * PM: meet, id=2610 -- WP: Lattice (order) -- Status: A
 * Paul August &#9742; 03:54, 9 May 2006 (UTC)


 * PM: meet continuous, id=8808new! -- WP guess: meet continuous -- Status:

06A15 Galois correspondences, closure operators

 * PM: Galois connection, id=6881 -- WP guess: Galois connection -- Status:

06A99 Miscellaneous

 * PM: ascending chain condition, id=982 -- WP: ascending chain condition -- Status: A
 * AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: covering relation, id=5573 -- WP guess: covering relation -- Status:


 * PM: dense (in a poset), id=3288 -- WP guess: dense (in a poset) -- Status:


 * PM: descending chain condition, id=984 -- WP: descending chain condition -- Status: A
 * AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: inductively ordered, id=6610 -- WP guess: inductively ordered -- Status: NC
 * Can also be merged into Zorn's lemma and redirect to that AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: locally finite poset, id=5572 -- WP guess: locally finite poset -- Status:


 * PM: order morphism, id=2619 -- WP: Monotonic function -- Status: NM
 * WP article needs to make clear that the two partial orders need not be the same AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: partial order, id=123 -- WP: partial order -- Status: A
 * WP article needs an easy explanaition using less than or equal notation AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: poset, id=132 -- WP: poset -- Status: NM
 * Example of elements that are not comparable. Also WP article would be more clear for non-maths if it would first give a short explanation using less than or equal notation, only then get into binary relations AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: quasi-order, id=3500 -- WP: Preorder -- Status: A
 * AdamSmithee 09:49, 6 January 2006 (UTC)


 * PM: lexicographic order, id=7005 -- WP guess: lexicographic order -- Status:


 * PM: Quasi-order is not defined uniformly, id=7499 -- WP guess: Quasi-order is not defined uniformly -- Status:


 * PM: ascending order, id=8176new! -- WP guess: ascending order -- Status:


 * PM: convex subgroup, id=9360new! -- WP guess: convex subgroup -- Status:


 * PM: descending order, id=8179new! -- WP guess: descending order -- Status:


 * PM: locally finite category, id=8756new! -- WP guess: locally finite category -- Status:


 * PM: Riesz interpolation property, id=9365new! -- WP guess: Riesz interpolation property -- Status:


 * PM: way below, id=8844new! -- WP guess: way below -- Status:

06B05 Structure theory

 * PM: bounded lattice, id=6755 -- WP: bounded lattice -- Status: NC
 * Should be copied to bounded lattice, which is now a redirect to lattice (order), but should be its own article. Paul August &#9742; 04:26, 9 May 2006 (UTC)


 * PM: complemented lattice, id=6754 -- WP: complemented lattice -- Status: NM
 * Paul August &#9742; 04:21, 9 May 2006 (UTC)


 * PM: example of non-complete lattice homomorphism, id=9253new! -- WP guess: example of non-complete lattice homomorphism -- Status:


 * PM: lattice homomorphism, id=7635new! -- WP guess: lattice homomorphism -- Status:

06B10 Ideals, congruence relations

 * PM: order in an algebra, id=4362 -- WP guess: order in an algebra -- Status:


 * PM: lattice filter, id=7782new! -- WP guess: lattice filter -- Status:


 * PM: lattice ideal, id=7781new! -- WP guess: lattice ideal -- Status:

06B20 Varieties of lattices

 * PM: partition lattice, id=5581 -- WP guess: partition lattice -- Status:


 * PM: partitions form a lattice, id=8982new! -- WP guess: partitions form a lattice -- Status:

06B23 Complete lattices, completions

 * PM: algebraic lattice, id=7951new! -- WP guess: algebraic lattice -- Status:


 * PM: compact element, id=7880new! -- WP guess: compact element -- Status:


 * PM: complete lattice homomorphism, id=9241new! -- WP guess: complete lattice homomorphism -- Status:


 * PM: example of a non-lattice homomorphism, id=9252new! -- WP guess: example of a non-lattice homomorphism -- Status:


 * PM: MacNeille completion, id=8152new! -- WP guess: MacNeille completion -- Status:


 * PM: uniformities on a set form a complete lattice, id=8690new! -- WP guess: uniformities on a set form a complete lattice -- Status:

06B25 Free lattices, projective lattices, word problems

 * PM: lattice polynomial, id=8692new! -- WP guess: lattice polynomial -- Status:

06B30 Topological lattices, order topologies

 * PM: topological lattice, id=7751new! -- WP guess: topological lattice -- Status:

06B35 Continuous lattices and posets, applications

 * PM: continuous poset, id=8942new! -- WP guess: continuous poset -- Status:


 * PM: domain, id=9062new! -- WP guess: domain -- Status:


 * PM: lattice of ideals, id=9275new! -- WP guess: lattice of ideals -- Status:


 * PM: Scott continuous, id=9072 -- WP: Scott continuous -- Status: A
 * PM article seems to be broken, can't even get TeX output for it. linas (talk) 15:32, 8 April 2008 (UTC)


 * PM: Scott topology, id=9063 -- WP: Scott topology -- Status: NM
 * linas (talk) 15:36, 8 April 2008 (UTC)

06B99 Miscellaneous

 * PM: proof of Schroeder-Bernstein theorem using Tarski-Knaster theorem, id=7367 -- WP: (none) -- Status: N


 * PM: Tarski-Knaster theorem, id=7366 -- WP: Knaster–Tarski theorem -- Status: A
 * Paul August &#9742; 05:12, 16 February 2007 (UTC)


 * PM: join irreducibility, id=7752new! -- WP guess: join irreducibility -- Status:


 * PM: special elements in a lattice, id=8923new! -- WP guess: special elements in a lattice -- Status:

06C05 Modular lattices, Desarguesian lattices

 * PM: modular lattice, id=2598 -- WP: modular lattice -- Status: NM
 * It might also be a good idea to create a separate article and link from Lattice (order) - AdamSmithee 15:57, 3 January 2006 (UTC)


 * PM: modular inequality, id=9210new! -- WP guess: modular inequality -- Status:


 * PM: nonmodular sublattice, id=9186new! -- WP guess: nonmodular sublattice -- Status:


 * PM: normal subgroup lattice is modular, id=7821new! -- WP guess: normal subgroup lattice is modular -- Status:

06C10 Semimodular lattices, geometric lattices

 * PM: semimodular lattice, id=7286 -- WP guess: semimodular lattice -- Status:

06C15 Complemented lattices, orthocomplemented lattices and posets

 * PM: relative complement, id=7852new! -- WP guess: relative complement -- Status:

06C20 Complemented modular lattices, continuous geometries

 * PM: continuous geometry, id=8921new! -- WP guess: continuous geometry -- Status:

06D05 Structure and representation theory

 * PM: Birkhoff prime ideal theorem, id=9325new! -- WP guess: Birkhoff prime ideal theorem -- Status:

06D10 Complete distributivity

 * PM: complete distributivity, id=7636new! -- WP guess: complete distributivity -- Status:

06D15 Pseudocomplemented lattices

 * PM: Brouwerian lattice, id=8733new! -- WP guess: Brouwerian lattice -- Status:


 * PM: pseudocomplement, id=7750new! -- WP guess: pseudocomplement -- Status:

06D20 Heyting algebras

 * PM: Heyting algebra, id=8734new! -- WP guess: Heyting algebra -- Status:

06D22 Frames, locales

 * PM: locale, id=8838new! -- WP guess: locale -- Status:

06D30 De Morgan algebras, Lukasiewicz algebras

 * PM: Kleene algebra, id=9453new! -- WP guess: Kleene algebra -- Status:


 * PM: Ockham algebra, id=9450new! -- WP guess: Ockham algebra -- Status:

06D99 Miscellaneous

 * PM: distributive, id=4493 -- WP: distributive -- Status: A
 * AdamSmithee 09:54, 6 January 2006 (UTC)


 * PM: distributive lattice, id=2596 -- WP: distributive lattice -- Status: A
 * AdamSmithee 09:54, 6 January 2006 (UTC)


 * PM: distributive inequalities, id=8830new! -- WP guess: distributive inequalities -- Status:


 * PM: generalized Boolean algebra, id=9451new! -- WP guess: generalized Boolean algebra -- Status:

06E20 Ring-theoretic properties

 * PM: ring hierarchy, id=8060new! -- WP guess: ring hierarchy -- Status:

06E99 Miscellaneous

 * PM: regular open set, id=6788 -- WP: regular open set -- Status: NC
 * Needs to be copied to regular open set which is now a redirect to Topology glossary. Paul August &#9742; 04:11, 9 May 2006 (UTC)

06F05 Ordered semigroups and monoids

 * PM: distributivity in po-groups, id=9379new! -- WP guess: distributivity in po-groups -- Status:


 * PM: partially ordered group, id=8922new! -- WP guess: partially ordered group -- Status:

06F07 Quantales

 * PM: quantale, id=9284new! -- WP guess: quantale -- Status:

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces

 * PM: absolute value in a vector lattice, id=9345new! -- WP guess: absolute value in a vector lattice -- Status:


 * PM: ordered space, id=9388new! -- WP guess: ordered space -- Status:


 * PM: ordered topological vector space, id=9347new! -- WP guess: ordered topological vector space -- Status:


 * PM: ordered vector space, id=8822new! -- WP guess: ordered vector space -- Status:


 * PM: rational rank of a group, id=9146new! -- WP guess: rational rank of a group -- Status:


 * PM: Riesz group, id=9464new! -- WP guess: Riesz group -- Status:


 * PM: solid set, id=9346new! -- WP guess: solid set -- Status:


 * PM: topological vector lattice, id=9356new! -- WP guess: topological vector lattice -- Status:


 * PM: vector lattice, id=9344new! -- WP guess: vector lattice -- Status: NM
 * linas (talk) 03:59, 29 November 2010 (UTC)

06F25 Ordered rings, algebras, modules

 * PM: ordered integral domain with well-ordered positive elements, id=6425 -- WP guess: ordered integral domain with well-ordered positive elements -- Status:


 * PM: ordered ring, id=445 -- WP: ordered ring -- Status: NM
 * Paul August &#9742; 04:04, 9 May 2006 (UTC)


 * PM: positivity in ordered ring, id=6424 -- WP: ordered ring -- Status: A
 * Paul August &#9742; 04:07, 9 May 2006 (UTC)


 * PM: well-ordering principle for natural numbers, id=244 -- WP : well-ordering principle -- Status: A
 * Paul August &#9742; 04:16, 9 May 2006 (UTC)


 * PM: \mathbb{C} is not an ordered field, id=8406new! -- WP guess: \mathbbC is not an ordered field -- Status:


 * PM: basic facts about ordered rings, id=8405new! -- WP guess: basic facts about ordered rings -- Status:


 * PM: partially ordered ring, id=9179new! -- WP guess: partially ordered ring -- Status:

06F30 Topological lattices, order topologies

 * PM: linear continuum, id=9638new! -- WP guess: linear continuum -- Status:

06F99 Miscellaneous

 * PM: latticoid, id=8695new! -- WP guess: latticoid -- Status: