Semigroups of order preserving partial transformations of a totally ordered set
نویسندگان
چکیده
منابع مشابه
Regular Elements of Some Semigroups of Order-Preserving Partial Transformations
Let X be a chain, OP (X) the order-preserving partial transformation semigroup on X and OI(X) the order-preserving 1–1 partial transformation semigroup on X. It is known that both OP (X) and OI(X) are regular semigroups. We extend these results by characterizing the regular elements of the semigroups OP (X,Y ), OI(X,Y ), OP (X,Y ) and OI(X,Y ) where ∅ = Y ⊆ X,OP (X,Y ) = {α ∈ OP (X) | ranα ⊆ Y ...
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The full order-preserving transformation semigroup, the orderpreserving partial transformation semigroup and the order-preserving one-to-one partial transformation semigroup on a poset X are denoted by OT (X), OP (X) and OI(X), respectively. It is well-known that for any posets X and Y , OT (X) ∼= OT (Y ) if and only if X and Y are either order-isomorphic or order-anti-isomorphic. The purpose o...
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Let Xn = {1, 2, . . . , n}. On a partial transformation α : Domα ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is | Dom α |, the height of α is | Im α |, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-p...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90158-5