scholarly journals ON SOME COMBINATORIAL RESULTS OF COLLAPSE IN PARTIAL TRANSFORMATION SEMIGROUPS

2020 ◽  
Vol 1 (3) ◽  
Keyword(s):  
Partial Transformation ◽  
Transformation Semigroups

Multiplicative invertibility characterization on star-like cyclicpoid CyPω*n finite partial transformation semigroups

2021 ◽  
Vol 10 (1) ◽  
pp. 45-55
Author(s):  
Sulaiman Awwal Akinwunmi ◽  
Morufu Mogbolagade Mogbonju ◽  
Adenike Olusola Adeniji
Keyword(s):  
Partial Transformation ◽  
Transformation Semigroups

scholarly journals Relative ranks of some partial transformation semigroups

2019 ◽  
Vol 43 (5) ◽  
pp. 2218-2225
Author(s):  
Ebru YİĞİT ◽  
Gonca AYIK ◽  
Hayrullah AYIK
Keyword(s):  
Partial Transformation ◽  
Transformation Semigroups

The (p,q)-potent ranks of certain semigroups of transformations

2016 ◽  
Vol 16 (07) ◽  
pp. 1750138
Author(s):  
Ping Zhao ◽  
Taijie You ◽  
Huabi Hu
Keyword(s):  
Partial Transformation ◽  
Transformation Semigroups ◽  
Generating Set ◽  
Idempotent Rank ◽  
Finite Set ◽  
Special Case

Let [Formula: see text] and [Formula: see text] be the partial transformation and the strictly partial transformation semigroups on the finite set [Formula: see text]. It is well known that the ranks of the semigroups [Formula: see text] and [Formula: see text] are [Formula: see text], for [Formula: see text], and [Formula: see text], for [Formula: see text], respectively. The idempotent rank, defined as the smallest number of idempotents generating set, of the semigroup [Formula: see text] has the same value as the rank. Idempotent can be seen as a special case (with [Formula: see text]) of [Formula: see text]-potent. In this paper, we determine the [Formula: see text]-potent ranks, defined as the smallest number of [Formula: see text]-potents generating set, of the semigroups [Formula: see text], for [Formula: see text], and [Formula: see text], for [Formula: see text].

scholarly journals PARTIAL ACTIONS OF INVERSE AND WEAKLY LEFT E-AMPLE SEMIGROUPS

2009 ◽  
Vol 86 (3) ◽  
pp. 355-377 ◽  
Author(s):  
VICTORIA GOULD ◽  
CHRISTOPHER HOLLINGS
Keyword(s):  
Unary Operation ◽  
Inverse Semigroups ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Partial Action ◽  
Ample Semigroup

AbstractWe introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α↦α+, where α+ is the identity map on the domain of α. We investigate the construction of ‘actions’ from such partial actions, making a connection with the FA-morphisms of Gomes. We observe that if the methods introduced in the monoid case by Megrelishvili and Schröder, and by the second author, are to be extended appropriately to the case of weakly left E-ample semigroups, then we must construct not global actions, but so-called incomplete actions. In particular, we show that a partial action of a weakly left E-ample semigroup is the restriction of an incomplete action. We specialize our approach to obtain corresponding results for inverse semigroups.

scholarly journals On Magnifying Elements in E-Preserving Partial Transformation Semigroups

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 160
Author(s):  
Thananya Kaewnoi ◽  
Montakarn Petapirak ◽  
Ronnason Chinram
Keyword(s):  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Necessary And Sufficient

Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X. In this paper, we consider the semigroup P ( X , E ) consisting of all E-preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X ) . The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X , E ) to be right or left magnifying.

Locally Maximal Idempotent-generated Subsemigroups of Finite Orientation-preserving Singular Partial Transformation Semigroups

2013 ◽  
Vol 20 (03) ◽  
pp. 435-442 ◽  
Author(s):  
Ping Zhao ◽  
Mei Yang
Keyword(s):  
Finite Order ◽  
Complete Classification ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Locally Maximal

In this paper we describe locally maximal idempotent-generated subsemigroups of finite orientation-preserving singular partial transformation semigroups SPOPn and obtain a complete classification. We also obtain a classification of locally maximal idempotent-generated subsemigroups of finite order-preserving singular partial transformation semigroups [Formula: see text] with respect to ≤k.

scholarly journals Congruences on Nilpotent-generated Partial Transformation Semigroups

2009 ◽  
Vol 16 (02) ◽  
pp. 229-242
Author(s):  
M. Paula O. Marques-Smith ◽  
R. P. Sullivan
Keyword(s):  
Partial Transformation ◽  
Transformation Semigroups

In 1987, Sullivan characterised the elements of the semigroup NP(X) generated by the nilpotents in P(X), the semigroup (under composition) consisting of all partial transformations of a set X; and in 1999, Marques-Smith and Sullivan determined all the ideals of NP(X) for arbitrary X. In this paper, we use that work to describe all the congruences on NP(X).

REGULARITY AND GREEN'S RELATIONS OF GENERALIZED PARTIAL TRANSFORMATION SEMIGROUPS

2008 ◽  
Vol 01 (03) ◽  
pp. 295-302 ◽  
Author(s):  
Ronnason Chinram
Keyword(s):  
Transformation Semigroup ◽  
Partial Transformation ◽  
Green’S Relations ◽  
Transformation Semigroups ◽  
Regular Elements ◽  
Green's Relations

Let X be any set and P(X) be the partial transformation semigroup on X. It is well-known that P(X) is regular. To generalize this, let X and Y be any sets and P(X, Y) be the set of all partial transformations from X to Y. For θ ∈ P(Y, X), let (P(X, Y), θ) be a semigroup (P(X, Y), *) where α * β = αθβ for all α, β ∈ P(X, Y). In this paper, we characterize the semigroup (P(X, Y), θ) to be regular, regular elements of the semigroup (P(X, Y), θ), [Formula: see text]-classes, [Formula: see text]-classes, [Formula: see text]-classes and [Formula: see text]-classes of the semigroup (P(X, Y), θ).

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