DSpace Collection:http://hdl.handle.net/10362/23292014-04-23T22:44:21Z2014-04-23T22:44:21ZNormally ordered semigroupsFernandes, Vítor H.http://hdl.handle.net/10362/55322011-04-20T11:13:40Z2008-01-01T00:00:00ZTitle: Normally ordered semigroups
Authors: Fernandes, Vítor H.
Abstract: In 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.
Description: Glasgow Mathematical Journal, nº 50 (2008), p. 325-3332008-01-01T00:00:00ZOn the monoids of transformations that preserve the order and a uniform partitionFernandes, Vítor H.Quinteiro, Teresa M.http://hdl.handle.net/10362/55312011-04-20T10:16:06Z2009-07-29T00:00:00ZTitle: On the monoids of transformations that preserve the order and a uniform partition
Authors: Fernandes, Vítor H.; Quinteiro, Teresa M.
Abstract: In this paper we consider the monoid O mxn of all order-preserving full transformations on a chain with mn elements that preserve a uniform m-partition and its submonoids O+ mxn and O− mxn of all extensive
transformations and of all co-extensive transformations, respectively. We give formulas for the number of elements of these monoids and determine their ranks. Moreover, we construct a bilateral semidirect product
decomposition of Omxn in terms of O− mxn and O+ mxn.
Description: Communications in Algebra2009-07-29T00:00:00ZThe cardinal of various monoids of transformations that preserve a uniform partitionFernandes, Vítor H.Quinteiro, Teresa M.http://hdl.handle.net/10362/55302011-04-19T14:58:14Z2010-07-30T00:00:00ZTitle: The cardinal of various monoids of transformations that preserve a uniform partition
Authors: Fernandes, Vítor H.; Quinteiro, Teresa M.
Abstract: In 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.
Description: Bulletin of the Malaysian Mathematical Sciences Society2010-07-30T00:00:00ZAutomorphisms of partial endomorphism semigroupsFernandes, Vítor H.Araújo, JJesus, Manuel MMaltcev, VMitchell, J Dhttp://hdl.handle.net/10362/55292011-04-19T14:15:22Z2009-01-01T00:00:00ZTitle: Automorphisms of partial endomorphism semigroups
Authors: Fernandes, Vítor H.; Araújo, J; Jesus, Manuel M; Maltcev, V; Mitchell, J D
Abstract: In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures
with a single m-ary relation for any m 2 N over a finite set.
We use this recipe to determine the automorphism groups of the following semigroups:the full transformation semigroup, the partial transformation semigroup, and the symmetric inverse semigroup, and their wreath products, partial endomorphisms of partially ordered sets, the full spectrum of semigroups of partial mappings preserving or reversing a linear or circular order. We also determine the automorphism groups of the so-called Madhaven semigroups as an application of the methods developed herein.
Description: Publicationes Mathematicae Debrecen2009-01-01T00:00:00Z