scholarly journals A PRESENTATION OF THE DUAL SYMMETRIC INVERSE MONOID

2008 ◽  
Vol 18 (02) ◽  
pp. 357-374 ◽  
Author(s):  
DAVID EASDOWN ◽  
JAMES EAST ◽  
D. G. FITZGERALD
Keyword(s):  
Inverse Monoid ◽  
Completely Regular ◽  
Regular Elements ◽  
Monoid Presentation ◽  
Symmetric Inverse Monoid ◽  
The Way

The dual symmetric inverse monoid [Formula: see text] is the inverse monoid of all isomorphisms between quotients of an n-set. We give a monoid presentation of [Formula: see text] and, along the way, establish criteria for a monoid to be inverse when it is generated by completely regular elements.

scholarly journals A presentation for the monoid of uniform block permutations

2003 ◽  
Vol 68 (2) ◽  
pp. 317-324 ◽  
Author(s):  
D. G. FitzGerald
Keyword(s):  
Symmetric Group ◽  
General Criterion ◽  
Inverse Monoid ◽  
Inverse Monoids ◽  
Natural Action ◽  
Monoid Presentation ◽  
Symmetric Inverse Monoid

The monoid n of uniform block permutations is the factorisable inverse monoid which arises from the natural action of the symmetric group on the join semilattice of equivalences on an n-set; it has been described in the literature as the factorisable part of the dual symmetric inverse monoid. The present paper gives and proves correct a monoid presentation forn. The methods involved make use of a general criterion for a monoid generated by a group and an idempotent to be inverse, the structure of factorisable inverse monoids, and presentations of the symmetric group and the join semilattice of equivalences on an n-set.

Left and right regular elements of the semigroups of transformations preserving an equivalence relation and a cross-section

2019 ◽  
Vol 12 (04) ◽  
pp. 1950058
Author(s):  
Nares Sawatraksa ◽  
Chaiwat Namnak ◽  
Ronnason Chinram
Keyword(s):  
Cross Section ◽  
Equivalence Relation ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Regular Elements ◽  
Left Regular ◽  
Completely Regular Semigroups ◽  
Cross Section Formula ◽  
Left And Right

Let [Formula: see text] be the semigroup of all transformations on a set [Formula: see text]. For an arbitrary equivalence relation [Formula: see text] on [Formula: see text] and a cross-section [Formula: see text] of the partition [Formula: see text] induced by [Formula: see text], let [Formula: see text] [Formula: see text] Then [Formula: see text] and [Formula: see text] are subsemigroups of [Formula: see text]. In this paper, we characterize left regular, right regular and completely regular elements of [Formula: see text] and [Formula: see text]. We also investigate conditions for which of these semigroups to be left regular, right regular and completely regular semigroups.

scholarly journals Unit regular inverse monoids and Cliford monoids

2018 ◽  
Vol 7 (2.13) ◽  
pp. 306
Author(s):  
Sreeja V K
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Group Element ◽  
Inverse Monoid ◽  
Completely Regular Semigroup ◽  
Clifford Semigroup ◽  
Inverse Monoids ◽  
Completely Regular ◽  
Group Of Units

Let S be a unit regular semigroup with group of units G = G(S) and semilattice of idempotents E = E(S). Then for every there is a such that Then both xu and ux are idempotents and we can write or .Thus every element of a unit regular inverse monoid is a product of a group element and an idempotent. It is evident that every L-class and every R-class contains exactly one idempotent where L and R are two of Greens relations. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. A completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. A Clifford semigroup is a completely regular inverse semigroup. Characterization of unit regular inverse monoids in terms of the group of units and the semilattice of idempotents is a problem often attempted and in this direction we have studied the structure of unit regular inverse monoids and Clifford monoids. 

scholarly journals Relative Abelian kernels of some classes of transformation monoids

2006 ◽  
Vol 73 (3) ◽  
pp. 375-404 ◽  
Author(s):  
E. Cordeiro ◽  
M. Delgado ◽  
V.H. Fernandes
Keyword(s):  
Abelian Groups ◽  
Inverse Monoid ◽  
Element Chain ◽  
Transformation Monoids ◽  
Symmetric Inverse Monoid

We consider the symmetric inverse monoid ℐn of an n-element chain and its inverse submonoids ℐn, ℐn, ℐn and ℘ℐn of all order-preserving, order-preserving or order-reversing, orientation-preserving and orientation-preserving or orientation-reversing transformations, respectively, and give descriptions of their Abelian kernels relative to decidable pseudovarieties of Abelian groups.

Presentation for the Partial Dual Symmetric Inverse Monoid

2015 ◽  
Vol 43 (4) ◽  
pp. 1621-1639 ◽  
Author(s):  
Ganna Kudryavtseva ◽  
Victor Maltcev ◽  
Abdullahi Umar
Keyword(s):  
Inverse Monoid ◽  
Symmetric Inverse Monoid

scholarly journals LARGEST 2-GENERATED SUBSEMIGROUPS OF THE SYMMETRIC INVERSE SEMIGROUP

2007 ◽  
Vol 50 (3) ◽  
pp. 551-561 ◽  
Author(s):  
J. M. André ◽  
V. H. Fernandes ◽  
J. D. Mitchell
Keyword(s):  
Inverse Semigroup ◽  
Inverse Monoid ◽  
Symmetric Inverse Semigroup ◽  
Symmetric Inverse Monoid ◽  
Element Set

AbstractThe symmetric inverse monoid $\mathcal{I}_{n}$ is the set of all partial permutations of an $n$-element set. The largest possible size of a $2$-generated subsemigroup of $\mathcal{I}_{n}$ is determined. Examples of semigroups with these sizes are given. Consequently, if $M(n)$ denotes this maximum, it is shown that $M(n)/|\mathcal{I}_{n}|\rightarrow1$ as $n\rightarrow\infty$. Furthermore, we deduce the known fact that $\mathcal{I}_{n}$ embeds as a local submonoid of an inverse $2$-generated subsemigroup of $\mathcal{I}_{n+1}$.

ON A NEW APPROACH TO THE DUAL SYMMETRIC INVERSE MONOID $\mathcal{I}_{X}^{\ast}$

2007 ◽  
Vol 17 (03) ◽  
pp. 567-591 ◽  
Author(s):  
VICTOR MALTCEV
Keyword(s):  
Inverse Semigroup ◽  
Cross Section ◽  
Inverse Monoid ◽  
Finite Sets ◽  
New Approach ◽  
Generating Set ◽  
Maximal Subsemigroups ◽  
Symmetric Inverse Semigroup ◽  
Transitive Representation ◽  
Symmetric Inverse Monoid

We construct the inverse partition semigroup[Formula: see text], isomorphic to the dual symmetric inverse monoid[Formula: see text], introduced in [6]. We give a convenient geometric illustration for elements of [Formula: see text]. We describe all maximal subsemigroups of [Formula: see text] and find a generating set for [Formula: see text] when X is finite. We prove that all the automorphisms of [Formula: see text] are inner. We show how to embed the symmetric inverse semigroup into the inverse partition one. For finite sets X, we establish that, up to equivalence, there is a unique faithful effective transitive representation of [Formula: see text], namely to [Formula: see text]. Finally, we construct an interesting [Formula: see text]-cross-section of [Formula: see text], which is reminiscent of [Formula: see text], the [Formula: see text]-cross-section of [Formula: see text], constructed in [4].

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