186 research outputs found
Presentations for monoids of finite partial isometries
In this paper we give presentations for the monoid of all
partial isometries on and for its submonoid
of all order-preserving partial isometries.Comment: 11 pages, submitte
On semigroups of endomorphisms of a chain with restricted range
Let be a finite or infinite chain and let be the monoid of all
endomorphisms of . In this paper, we describe the largest regular
subsemigroup of and Green's relations on . In fact, more
generally, if is a nonempty subset of and the subsemigroup of
of all elements with range contained in , we characterize the largest
regular subsemigroup of and Green's relations on . Moreover,
for finite chains, we determine when two semigroups of the type are
isomorphic and calculate their ranks.Comment: To appear in Semigroup Foru
On divisors of pseudovarieties generated by some classes of full transformation semigroups
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
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
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
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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