Distributive Closed Inverse Subsemigroup Lattices

1997 ◽  
Vol 55 (3) ◽  
pp. 332-354
Author(s):  
Kyeong Hee Cheong
Keyword(s):  
Inverse Subsemigroup

scholarly journals On quasi-orthodox semigroups with inverse transversals

1997 ◽  
Vol 40 (3) ◽  
pp. 505-514 ◽  
Author(s):  
T. S. Blyth ◽  
M. H. Almeida Santos
Keyword(s):  
Regular Semigroup ◽  
Inverse Transversal ◽  
Inverse Subsemigroup ◽  
Orthodox Semigroups

An inverse transversal of a regular semigroup S is an inverse subsemigroup So that contains precisely one inverse of each element of S. Here we consider the case where S is quasi-orthodox. We give natural characterisations of such semigroups and consider various properties of congruences.

scholarly journals A simplistic approach to inverse transversals

1996 ◽  
Vol 39 (1) ◽  
pp. 57-69 ◽  
Author(s):  
T. S. Blyth ◽  
M. H. Almeida Santos
Keyword(s):  
Regular Semigroup ◽  
Inverse Transversal ◽  
Inverse Subsemigroup

An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element of S. In the literature there are three known types of inverse transversal, namely those that are multiplicative, those that are weakly multiplicative, and those that form quasi-ideals. Here, by considering natural ways in which certain words can be simplified, we reveal four new types of inverse transversal. All of these can be illustrated nicely in examples that are based on 2 × 2 matrices.

Maximal inverse subsemigroups of the semigroup of all full transformations satisfying x ≈ x3

2016 ◽  
Vol 09 (01) ◽  
pp. 1650042
Author(s):  
Somnuek Worawiset
Keyword(s):  
Natural Number ◽  
Transformation Semigroup ◽  
Inverse Semigroups ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Inverse Subsemigroup ◽  
Number Formula ◽  
Inverse Subsemigroups ◽  
Text Element ◽  
Element Set

We classify the maximal Clifford inverse subsemigroups [Formula: see text] of the full transformation semigroup [Formula: see text] on an [Formula: see text]-element set with [Formula: see text] for all [Formula: see text]. This classification differs from the already known classifications of Clifford inverse semigroups, it provides an algorithm for its construction. For a given natural number [Formula: see text], we find also the largest size of an inverse subsemigroup [Formula: see text] of [Formula: see text] satisfying [Formula: see text] with least rank [Formula: see text] for any element in [Formula: see text].

scholarly journals EMBEDDING ℐn IN A 2-GENERATOR INVERSE SUBSEMIGROUP OF ℐn+2

2002 ◽  
Vol 45 (1) ◽  
pp. 1-4 ◽  
Author(s):  
D. B. McAlister ◽  
J. B. Stephen ◽  
A. S. Vernitski
Keyword(s):  
Inverse Semigroup ◽  
Subject Classification ◽  
Inverse Subsemigroup

AbstractGiven an integer $n$, we show that $\mathcal{I}_{n}$ embeds in a 2-generated subsemigroup of $\mathcal{I}_{n+2}$, which is an inverse semigroup. An immediate consequence of this result is the following, which is analogous to the case for groups and semigroups: every finite inverse semigroup may be embedded in a finite 2-generated semigroup which is an inverse semigroup.AMS 2000 Mathematics subject classification: Primary 20M18. Secondary 20M20

Regular semigroups with a multiplicative inverse transversal

1982 ◽  
Vol 92 (3-4) ◽  
pp. 253-270 ◽  
Author(s):  
T. S. Blyth ◽  
R. McFadden
Keyword(s):  
Regular Semigroup ◽  
Inverse Transversal ◽  
Multiplicative Inverse ◽  
Multiplicative Property ◽  
Regular Semigroups ◽  
Inverse Subsemigroup

SynopsisBy an inverse transversal of a regular semigroup S we mean an inverse subsemigroup that contains a single inverse of every element of S. A certain multiplicative property (which in the case of a band is equivalent to normality) is imposed on an inverse transversal and a complete description of the structure of S is obtained.

scholarly journals On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers

2019 ◽  
Vol 11 (2) ◽  
pp. 296-310
Author(s):  
O.V. Gutik ◽  
A.S. Savchuk
Keyword(s):  
Additive Group ◽  
Group Congruence ◽  
Topological Semigroups ◽  
Inverse Subsemigroup ◽  
Minimum Group ◽  
Identity Congruence ◽  
Positive Integers ◽  
Quotient Semigroup

In this paper we study submonoids of the monoid $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ of almost monotone injective co-finite partial selfmaps of positive integers $\mathbb{N}$. Let $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ be a submonoid of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ which consists of cofinite monotone partial bijections of $\mathbb{N}$ and $\mathscr{C}_{\mathbb{N}}$ be a subsemigroup of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ which is generated by the partial shift $n\mapsto n+1$ and its inverse partial map. We show that every automorphism of a full inverse subsemigroup of $\mathscr{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ which contains the semigroup $\mathscr{C}_{\mathbb{N}}$ is the identity map. We construct a submonoid $\mathbf{I}\mathbb{N}_{\infty}^{[\underline{1}]}$ of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ with the following property: if $S$ is an inverse submonoid of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathbf{I}\mathbb{N}_{\infty}^{[\underline{1}]}$ as a submonoid, then every non-identity congruence $\mathfrak{C}$ on $S$ is a group congruence. We show that if $S$ is an inverse submonoid of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathscr{C}_{\mathbb{N}}$ as a submonoid then $S$ is simple and the quotient semigroup $S/\mathfrak{C}_{\mathbf{mg}}$, where $\mathfrak{C}_{\mathbf{mg}}$ is the minimum group congruence on $S$, is isomorphic to the additive group of integers. Also, we study topologizations of inverse submonoids of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ which contain $\mathscr{C}_{\mathbb{N}}$ and embeddings of such semigroups into compact-like topological semigroups.

The variety of unary semigroups with associate inverse subsemigroup

2013 ◽  
Vol 89 (1) ◽  
pp. 68-71 ◽  
Author(s):  
B. Billhardt ◽  
E. Giraldes ◽  
P. Marques-Smith ◽  
P. Mendes Martins
Keyword(s):  
Inverse Subsemigroup ◽  
Associate Inverse Subsemigroup

The group of units as a maximal inverse subsemigroup

1982 ◽  
Vol 25 (1) ◽  
pp. 381-382
Author(s):  
Bridget B. Baird
Keyword(s):  
Group Of Units ◽  
Inverse Subsemigroup

Ideal extensions of locally inverse semigroups

2008 ◽  
Vol 45 (3) ◽  
pp. 395-409 ◽  
Author(s):  
Francis Pastijn ◽  
Luís Oliveira
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Inverse Subsemigroup ◽  
Locally Inverse Semigroup ◽  
Locally Inverse Semigroups

The translational hull of a locally inverse semigroup has a largest locally inverse subsemigroup containing the inner part. A construction is given for ideal extensions within the class of all locally inverse semigroups.

scholarly journals Inverse semigroups generated by nilpotent transformations

1984 ◽  
Vol 99 (1-2) ◽  
pp. 153-162 ◽  
Author(s):  
John M. Howie ◽  
M. Paula O. Marques-Smith
Keyword(s):  
Inverse Semigroup ◽  
Homomorphic Image ◽  
Inverse Semigroups ◽  
Nilpotent Elements ◽  
Inverse Subsemigroup ◽  
Symmetric Inverse Semigroup ◽  
Infinite Cardinality ◽  
Index 2 ◽  
Rees Quotient ◽  
The Ideal

SynopsisLet X be a set with infinite cardinality m and let B be the Baer-Levi semigroup, consisting of all one-one mappings a:X→X for which ∣X/Xα∣ = m. Let Km=<B 1B>, the inverse subsemigroup of the symmetric inverse semigroup ℐ(X) generated by all products β−γ, with β,γ∈B. Then Km = <N2>, where N2 is the subset of ℐ(X) consisting of all nilpotent elements of index 2. Moreover, Km has 2-nilpotent-depth 3, in the sense that Let Pm be the ideal {α∈Km: ∣dom α∣<m} in Km and let Lm be the Rees quotient Km/Pm. Then Lm is a 0-bisimple, 2-nilpotent-generated inverse semigroup with 2-nilpotent-depth 3. The minimum non-trivial homomorphic image of Lm also has these properties and is congruence-free.

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