noun
Meaning 1
A partially ordered set.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, order-theory, sciences, set-theory
Examples
- 1973, Barbara L. Osofsky, Homological Dimensions of Modules, American Mathematical Society, →ISBN, page 76, 42. Definition. A poset (partially ordered set) (X, ≤) (usually written just X) is a set X together with a transitive, antisymmetric relation ≤ on X. 43. Definition. A linearly ordered set or chain is a poset (X, ≤), such that ∀a, b ∈ X, either a ≤ b or b ≤ a or a = b.
- 1998, Yuri A. Drozd, Representations of bisected posets and reflection functors, Idun Reiten, Sverre O. Smalø, Øyvind Solberg (editors), Algebras and Modules II, American Mathematical Society (for Canadian Mathematical Society), page 153, We construct a complete set of reflection functors for the representations of posets and prove that they really have the usual properties. In particular, when the poset is of finite representation type, all of its indecomposable representations can be obtained from some "trivial" ones via relations. To define such reflection functors, a wider class of matrix problem is introduced, called "representations of bisected posets".
Meaning relationships
Synonyms: none provided
Antonyms: none provided