On right unipotent semigroups

Venkatesan, P. S.

doi:10.2140/pjm.1976.63.555

Cited by 11 publications

(6 citation statements)

References 6 publications

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“…Therefore xex' = xx'exx' = xx'e, and (Qx) is satisfied for all xeS. This implies that S is a union of groups and (x, xx -1 )ej3 for all x € S [12]. Hence O ( x , y ) 6 « .…”

Section: Theorem 4 Let S Be a Right Unipotent Semigroup And Let E = mentioning

confidence: 93%

“…Then (i) fef = fe for any two idempotents e, f of S, and (ii) aa' = aa* for any a', a* in V(a) [11]. Further, /3 is the greatest idempotent-separating congruence on S [12]. Since /3 = 8 follows from the definition of S, we have /x = /?…”

Section: Theorem 2 Let S Be An Orthodox Semigroup Write L = S/n Mmentioning

confidence: 97%

“…Then (i) {Qx) implies (Px) for any x in S, (ii) S is a union of groups if and only if (Px) is satisfied for all x in S and (iii) S//3 is isomorphic to E if and only if (Ox) is satisfied for all x in S [12].…”

Section: Theorem 4 Let S Be a Right Unipotent Semigroup And Let E = mentioning

confidence: 99%

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On right unipotent semigroups II

Venkatesan

1978

Glasgow Math. J.

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“…Therefore xex' = xx'exx' = xx'e, and (Qx) is satisfied for all xeS. This implies that S is a union of groups and (x, xx -1 )ej3 for all x € S [12]. Hence O ( x , y ) 6 « .…”

Section: Theorem 4 Let S Be a Right Unipotent Semigroup And Let E = mentioning

confidence: 93%

Section: Theorem 2 Let S Be An Orthodox Semigroup Write L = S/n Mmentioning

confidence: 97%

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On right unipotent semigroups II

Venkatesan

1978

Glasgow Math. J.

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“…For basic concept we refer the reader to [13,11,18]. Lets us recall that an element α ∈ CT n is regular if and only if Ker α has convex transversal.…”

Section: Regular Elements Of Ct Nmentioning

confidence: 99%

On certain semigroups of full contractions of a finite chain

Umar¹,

Zubairu²

2018

Preprint

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“…R-unipotent semigroups have been studied by different authors including Venkatesan [15,16] and Edwards [2,3].…”

Section: Introductionmentioning

confidence: 99%

On left quasinormal orthodox semigroups

Gomes

1983

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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SynopsisThe existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroup S is locally inverse and orthodox if and only if there exists a local isomorphism from S onto an inverse semigroup T.In this paper, we show the existence of a smallest R-unipotent congruence ρ on an orthodox semigroup S and give its expression in the case where S is also left quasinormal. Finally, we prove that a regular semigroup S is left quasinormal and orthodox if and only if there exists a local isomorphism from S onto an R-unipotent semigroup T.

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On right unipotent semigroups

Cited by 11 publications

References 6 publications

On right unipotent semigroups II

On right unipotent semigroups II

On certain semigroups of full contractions of a finite chain

On left quasinormal orthodox semigroups

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