186 research outputs found

    Presentations for monoids of finite partial isometries

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    In this paper we give presentations for the monoid DPn\mathcal{DP}_n of all partial isometries on {1,,n}\{1,\ldots,n\} and for its submonoid ODPn\mathcal{ODP}_n of all order-preserving partial isometries.Comment: 11 pages, submitte

    On semigroups of endomorphisms of a chain with restricted range

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    Let XX be a finite or infinite chain and let O(X)O(X) be the monoid of all endomorphisms of XX. In this paper, we describe the largest regular subsemigroup of O(X)O(X) and Green's relations on O(X)O(X). In fact, more generally, if YY is a nonempty subset of XX and O(X,Y)O(X,Y) the subsemigroup of O(X)O(X) of all elements with range contained in YY, we characterize the largest regular subsemigroup of O(X,Y)O(X,Y) and Green's relations on O(X,Y)O(X,Y). Moreover, for finite chains, we determine when two semigroups of the type O(X,Y)O(X,Y) are isomorphic and calculate their ranks.Comment: To appear in Semigroup Foru

    On divisors of pseudovarieties generated by some classes of full transformation semigroups

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    Algebra Colloquium, 15 (2008), p. 581–588In this paper we present a division theorem for the pseudovariety of semigroups OD [OR] generated by all semigroups of order-preserving or order-reversing [orientationpreserving or orientation-reversing] full transformations on a finite chain

    Normally ordered semigroups

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    Glasgow Mathematical Journal, nº 50 (2008), p. 325-333In this paper we introduce the notion of normally ordered block-group as a natural extension of the notion of normally ordered inverse semigroup considered previously by the author. We prove that the class NOS of all normally ordered blockgroups forms a pseudovariety of semigroups and, by using theMunn representation of a block-group, we deduce the decompositions in Mal’cev products NOS = EI m POI and NOS \ A = N m POI, where A, EI and N denote the pseudovarieties of all aperiodic semigroups, all semigroups with just one idempotent and all nilpotent semigroups, respectively, and POI denotes the pseudovariety of semigroups generated all semigroups of injective order-preserving partial transformations on a finite chain. These relations are obtained after showing that BG = EI m Ecom = N m Ecom, where BG and Ecom denote the pseudovarieties of all block-groups and all semigroups with commuting idempotents, respectively

    The cardinal of various monoids of transformations that preserve a uniform partition

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    Bulletin of the Malaysian Mathematical Sciences SocietyIn this paper we give formulas for the number of elements of the monoids OR mxn of all full transformations on a nite chain with mn elements that preserve a uniform m-partition and preserve or reverse the orientation and for its submonoids OD mxn of all order-preserving or order-reversing elements, OP mxn of all orientation- preserving elements, O mxn of all order-preserving elements, O+ mxn of all extensive order-preserving elements and O- mxn of all co-extensive order-preserving elements

    The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence

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    Grant No. SRF-PRG-2557-02.A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.authorsversionpublishe
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