Centralizers of full injective transformations in the symmetric inverse semigroup

2017 ◽  
Vol 96 (3) ◽  
pp. 474-488 ◽  
Author(s):  
Janusz Konieczny
Keyword(s):  
Inverse Semigroup ◽  
Symmetric Inverse Semigroup

scholarly journals Congruences induced by transitive representations of inverse semigroups

1987 ◽  
Vol 29 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Mario Petrich ◽  
Stuart Rankin
Keyword(s):  
General Theory ◽  
Inverse Semigroup ◽  
Symmetric Group ◽  
Transitive Group ◽  
Inverse Semigroups ◽  
Group Representations ◽  
Symmetric Inverse Semigroup ◽  
The Right ◽  
Special Case

Transitive group representations have their analogue for inverse semigroups as discovered by Schein [7]. The right cosets in the group case find their counterpart in the right ω-cosets and the symmetric inverse semigroup plays the role of the symmetric group. The general theory developed by Schein admits a special case discovered independently by Ponizovskiǐ [4] and Reilly [5]. For a discussion of this topic, see [1, §7.3] and [2, Chapter IV].

scholarly journals EMBEDDINGS IN COSET MONOIDS

2008 ◽  
Vol 85 (1) ◽  
pp. 75-80
Author(s):  
JAMES EAST
Keyword(s):  
Semigroup Forum ◽  
Inverse Semigroup ◽  
Simple Proof ◽  
Inverse Semigroups ◽  
Sufficient Condition ◽  
Simple Description ◽  
Group Of Units ◽  
Finite Monoids ◽  
Finite Set ◽  
Symmetric Inverse Semigroup

AbstractA submonoid S of a monoid M is said to be cofull if it contains the group of units of M. We extract from the work of Easdown, East and FitzGerald (2002) a sufficient condition for a monoid to embed as a cofull submonoid of the coset monoid of its group of units, and show further that this condition is necessary. This yields a simple description of the class of finite monoids which embed in the coset monoids of their group of units. We apply our results to give a simple proof of the result of McAlister [D. B. McAlister, ‘Embedding inverse semigroups in coset semigroups’, Semigroup Forum20 (1980), 255–267] which states that the symmetric inverse semigroup on a finite set X does not embed in the coset monoid of the symmetric group on X. We also explore examples, which are necessarily infinite, of embeddings whose images are not cofull.

PARABOLIC SUBGROUPS AND CUSPIDAL REPRESENTATIONS OF FINITE MONOIDS

1991 ◽  
Vol 01 (01) ◽  
pp. 33-47 ◽  
Author(s):  
JAN OKNIŃSKI ◽  
MOHAN S. PUTCHA
Keyword(s):  
Inverse Semigroup ◽  
Finite Groups ◽  
Special Class ◽  
Semigroup Algebra ◽  
Parabolic Subgroups ◽  
Finite Monoids ◽  
Representations Of Finite Groups ◽  
Symmetric Inverse Semigroup ◽  
Complex Semigroup ◽  
Cuspidal Representations

This paper is mostly concerned with arbitrary finite monoids M with the complex semigroup algebra [Formula: see text] semisimple. Using the 1942 work of Clifford, we develop for these monoids a theory of cuspidal representations. Harish-Chandra's philosophy of cuspidal representations of finite groups can then be derived with an appropriate specialization. For [Formula: see text], we use Solomon's Hecke algebra to obtain a correspondence between the 'simple' representations of [Formula: see text] and the representations of the symmetric inverse semigroup. We also prove a semisimplicity theorem for a special class of finite monoids of the type which was earlier used by the authors to prove the semisimplicity of [Formula: see text].

scholarly journals On the semigroup of all partial fence-preserving injections on a finite set

2017 ◽  
Vol 16 (12) ◽  
pp. 1750223 ◽  
Author(s):  
Ilinka Dimitrova ◽  
Jörg Koppitz
Keyword(s):  
Inverse Semigroup ◽  
Transformation Formula ◽  
Green’S Relations ◽  
Generating Set ◽  
Regular Elements ◽  
Green's Relations ◽  
Finite Set ◽  
Symmetric Inverse Semigroup ◽  
Text Element ◽  
Element Set

For [Formula: see text], let [Formula: see text] be an [Formula: see text]-element set and let [Formula: see text] be a fence, also called a zigzag poset. As usual, we denote by [Formula: see text] the symmetric inverse semigroup on [Formula: see text]. We say that a transformation [Formula: see text] is fence-preserving if [Formula: see text] implies that [Formula: see text], for all [Formula: see text] in the domain of [Formula: see text]. In this paper, we study the semigroup [Formula: see text] of all partial fence-preserving injections of [Formula: see text] and its subsemigroup [Formula: see text]. Clearly, [Formula: see text] is an inverse semigroup and contains all regular elements of [Formula: see text] We characterize the Green’s relations for the semigroup [Formula: see text]. Further, we prove that the semigroup [Formula: see text] is generated by its elements with rank [Formula: see text]. Moreover, for [Formula: see text], we find the least generating set and calculate the rank of [Formula: see text].

On the semigroups of partial one-to-one order-decreasing finite transformations

1993 ◽  
Vol 123 (2) ◽  
pp. 355-363 ◽  
Author(s):  
Abdullahi Umar
Keyword(s):  
Inverse Semigroup ◽  
Symmetric Inverse Semigroup ◽  
One To One

SynopsisLet In be the symmetric inverse semigroup on Xn = {1,…, n}, let Sln be the subsemigroup of strictly partial one-to-one self-maps of Xn and let = { α ∊ SIn: x} ≦ x = U = ∅= be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. In this paper it is shown that is an (irregular, for n ≧ 2) type A semigroup with n D*-classes and D* = I*. Further, it is shown that is generated by the n(n + l)/2 quasi-idempotents in

scholarly journals PARTIAL ORDERS ON PARTIAL BAER–LEVI SEMIGROUPS

2010 ◽  
Vol 81 (2) ◽  
pp. 195-207 ◽  
Author(s):  
BOORAPA SINGHA ◽  
JINTANA SANWONG ◽  
R. P. SULLIVAN
Keyword(s):  
Inverse Semigroup ◽  
Partial Order ◽  
Partial Orders ◽  
The Other ◽  
Natural Order ◽  
Natural Partial Order ◽  
Transformation Semigroups ◽  
Minimal Elements ◽  
Symmetric Inverse Semigroup ◽  
Containment Order

AbstractMarques-Smith and Sullivan [‘Partial orders on transformation semigroups’, Monatsh. Math.140 (2003), 103–118] studied various properties of two partial orders on P(X), the semigroup (under composition) consisting of all partial transformations of an arbitrary set X. One partial order was the ‘containment order’: namely, if α,β∈P(X) then α⊆β means xα=xβ for all x∈dom α, the domain of α. The other order was the so-called ‘natural order’ defined by Mitsch [‘A natural partial order for semigroups’, Proc. Amer. Math. Soc.97(3) (1986), 384–388] for any semigroup. In this paper, we consider these and other orders defined on the symmetric inverse semigroup I(X) and the partial Baer–Levi semigroup PS(q). We show that there are surprising differences between the orders on these semigroups, concerned with their compatibility with respect to composition and the existence of maximal and minimal elements.

scholarly journals The commuting graph of the symmetric inverse semigroup

2015 ◽  
Vol 207 (1) ◽  
pp. 103-149 ◽  
Author(s):  
João Araújo ◽  
Wolfram Bentz ◽  
Konieczny Janusz
Keyword(s):  
Inverse Semigroup ◽  
Commuting Graph ◽  
Symmetric Inverse Semigroup
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