58 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
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 idempotent-separating degree of a block-group
Semigroup Forum, nÂş76 (2008), pg.579-583In this paper we describe the least non-negative integer n such that
there exists an idempotent-separating homomorphism from a finite block-group S
into the monoid of all partial transformations of a set with n elements. In particular,
as for a fundamental semigroup S this number coincides with the smallest size
of a set for which S can be faithfully represented by partial transformations, we
obtain a generalization of Easdown’s result established for fundamental finite inverse
semigroups
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
The cardinal of various monoids of transformations that preserve a uniform partition
In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements
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
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