44 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
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
On the monoids of transformations that preserve the order and a uniform partition
Communications in AlgebraIn 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
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
On the monoids of transformations that preserve the order and a uniform partition
In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+)
Bilateral semidirect product decompositions of transformation monoids
In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids