Generalised partial transformation semigroups

It is well-known that for any set X, px, the semigroup of all partial transformations on X, can be embedded in Jx∪a for some a ∉ X (see for example Clifford and Preston (1967) and Ljapin (1963)). Recently Magill (1967) has considered a special case of what we call ‘generalised partial transformation semigroups’. We show here that any such semigroup can always be embedded in a full transformation smigroup in which the operation is not in general equal to the usual composition of mappinas. We then examine conditions under which such a semigroup, (J x, θ), is isomorphic to the semigroup, under composition, of all transformations on the same set X.

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

Journal of Algebra and Its Applications ◽

10.1142/s0219498817501389 ◽

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].

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Flows on Classes of Regular Semigroups and Cauchy Categories

Journal of Mathematics ◽

10.1155/2019/8027391 ◽

2019 ◽

Vol 2019 ◽

pp. 1-9

Author(s):

Suha Ahmed Wazzan

Keyword(s):

General Structure ◽

Transformation Semigroups ◽

Full Transformation ◽

Regular Semigroups ◽

Rees Matrix Semigroups ◽

Completely Simple Semigroups ◽

Special Case ◽

Brandt Semigroups ◽

Matrix Semigroups ◽

Completely Simple

We consider the structure of the flow monoid for some classes of regular semigroups (which are special case of flows on categories) and for Cauchy categories. In detail, we characterize flows for Rees matrix semigroups, rectangular bands, and full transformation semigroups and also describe the Cauchy categories for some classes of regular semigroups such as completely simple semigroups, Brandt semigroups, and rectangular bands. In fact, we obtain a general structure for the flow monoids on Cauchy categories.

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Automorphisms of normal partial transformation semigroups

Glasgow Mathematical Journal ◽

10.1017/s0017089500006790 ◽

1987 ◽

Vol 29 (2) ◽

pp. 149-157 ◽

Cited By ~ 12

Author(s):

Inessa Levi

Keyword(s):

Symmetric Group ◽

Transformation Semigroup ◽

Partial Transformation ◽

Transformation Semigroups ◽

Full Transformation ◽

Full Transformation Semigroup ◽

Infinite Set

We let X be an arbitrary infinite set. A semigroup S of total or partial transformations of X is called -normal if hSh-1 = S, for all h in , the symmetric group on X. For example, the full transformation semigroup , the semigroup of all partial transformations , the semigroup of all 1–1 partial transformations and all ideals of and are -normal.

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Skew Pairs of Idempotents in Partial Transformation Semigroups

Mathematics ◽

10.3390/math10010002 ◽

2021 ◽

Vol 10 (1) ◽

pp. 2

Author(s):

Panuwat Luangchaisri ◽

Thawhat Changphas

Keyword(s):

Regular Semigroup ◽

Transformation Semigroup ◽

Acta Math ◽

Partial Transformation ◽

Transformation Semigroups ◽

Full Transformation ◽

Full Transformation Semigroup ◽

Left Regular

Let S be a regular semigroup. A pair (e,f) of idempotents of S is said to be a skew pair of idempotents if fe is idempotent, but ef is not. T. S. Blyth and M. H. Almeida (T. S. Blyth and M. H. Almeida, skew pair of idempotents in transformation semigroups, Acta Math. Sin. (English Series), 22 (2006), 1705–1714) gave a characterization of four types of skew pairs—those that are strong, left regular, right regular, and discrete—existing in a full transformation semigroup T(X). In this paper, we do in this line for partial transformation semigroups.

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

Pure Mathematical Sciences ◽

10.12988/pms.2021.91276 ◽

2021 ◽

Vol 10 (1) ◽

pp. 45-55

Author(s):

Sulaiman Awwal Akinwunmi ◽

Morufu Mogbolagade Mogbonju ◽

Adenike Olusola Adeniji

Keyword(s):

Partial Transformation ◽

Transformation Semigroups

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On automorphisms of monotone transformation posemigroups

Asian-European Journal of Mathematics ◽

10.1142/s1793557122500322 ◽

2021 ◽

pp. 2250032

Author(s):

Dilawar Juneed Mir ◽

Aftab Hussain Shah ◽

Shabir Ahmad Ahanger

Keyword(s):

Partial Transformation ◽

Monotone Transformation ◽

Full Transformation ◽

Simple Generalization

In this paper, we provide a simple generalization of results of Sullivan for [Formula: see text] the full transformation monotone pomonoid and for [Formula: see text] the partial transformation monotone pomonoid by showing that every automorphism of [Formula: see text] and [Formula: see text] is inner induced by the elements of [Formula: see text] the pogroup of all ordered bijections on [Formula: see text]. We also show that [Formula: see text] is isomorphic to [Formula: see text]. Finally, we apply these results to get some more results in this direction.

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