Definition, Betydelse, Synonymer & Anagram | Engelska ordet POSET

Definition av POSET

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Exempel på hur du använder POSET i en mening

• In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements.
• This implies that any filter that properly contains an ultrafilter has to be equal to the whole poset.
• Zeta function of an incidence algebra, a function that maps every interval of a poset to the constant value 1.
• More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.
• Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, Subtract a square, Notakto, and poset games.
• A common element of such axiomatizations is the assumption, shared with inclusion, that the part-whole relation orders its universe, meaning that everything is a part of itself (reflexivity), that a part of a part of a whole is itself a part of that whole (transitivity), and that two distinct entities cannot each be a part of the other (antisymmetry), thus forming a poset.
• From the monotonicity and continuity of relation composition, it follows immediately that the set of bisimulations is closed under unions (joins in the poset of relations), and a simple algebraic calculation shows that the relation of bisimilarity—the join of all bisimulations—is an equivalence relation.
• A closure operator on the poset P is a function C : P → P that is monotone, idempotent, and satisfies C(x) ≥ x for all x in P.
• The categorical concept of limit-preserving and limit-reflecting functors is in complete harmony with order theory, since orders can be considered as small categories defined as poset categories with defined additional structure.
• In mathematics, specifically abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules.
• The Noetherian condition can also be defined on bimodule structures as well: a Noetherian bimodule is a bimodule whose poset of sub-bimodules satisfies the ascending chain condition.
• In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).
• Most classes of greedoids have many equivalent definitions in terms of set system, language, poset, simplicial complex, and so on.
• An opposite notion to a clutter is an abstract simplicial complex, where every subset of an edge is contained in the hypergraph; this is an order ideal in the poset of subsets of V.
• An algebraic model of boolean bunched logic is a poset that is a Boolean algebra and that carries an additional residuated commutative monoid structure.
• We can recover the poset S from the nerve NS and the category C from the nerve NC; in this sense simplicial sets generalize posets and categories.
• The Hasse diagram defines the unique poset and therefore fully captures the structure of the polytope.
• The cofinal relation over partially ordered sets ("posets") is reflexive: every poset is cofinal in itself.
• – a graded poset is analogous to a prewellordering with a norm, replacing a map to the ordinals with a map to the natural numbers.
• Prewellordering – a prewellordering with a norm is analogous to a graded poset, replacing a map to the integers with a map to the ordinals.

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