Orders in completely regular semigroups

Petrich, Mario

doi:10.1112/s0025579300014455

Cited by 3 publications

(3 citation statements)

References 12 publications

(22 reference statements)

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“…x τ γ a (10) and thus xpa 2 τ γ a which yields the first relation in (9). Now a τ γ b and q τ γ bϕ β,αβ by condition (A ) easily yield that xpa λ γ yqb.…”

Section: By Lemma 43 We Getmentioning

confidence: 88%

On Orders in Normal Cryptogroups

Petrich¹

2011

Results. Math.

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A semigroup S is an order in a semigroup Q if every element of Q is of the form q = a −1 b = cd −1 for some a, b, c, d ∈ S, where a −1 and d −1 are inverses within group H-classes of Q. We study orders in normal cryptogroups based on considering the restrictions of Green's relations of Q to S. This produces certain relations which help us to gain an overview of all normal cryptogroups Q in which S is an order. Distinguished orders play an important role in this context. Mathematics Subject Classification (2010). 20M10.

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“…x τ γ a (10) and thus xpa 2 τ γ a which yields the first relation in (9). Now a τ γ b and q τ γ bϕ β,αβ by condition (A ) easily yield that xpa λ γ yqb.…”

Section: By Lemma 43 We Getmentioning

confidence: 88%

On Orders in Normal Cryptogroups

Petrich¹

2011

Results. Math.

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“…Completely regular semigroups have been explored extensively. Especially, Petrich, M. [7] and Howie, J.M. [6] generalized many properties of completely regular semigroups which were investigated by some algebraists such as Lajos, S. and Jones, P.R.…”

Section: Introductionmentioning

confidence: 99%

“…[6,7]) Let S be a completely simple semigroup, then ab ∈ R a ∩ L b for all a, b ∈ S and κ = {L, R, H, D} is a congruence on S.…”

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confidence: 99%

Properties of GV-semigroups

Wang¹

2016

ijcms

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Orders and Straight Left Orders in Completely Regular Semigroups

Gould

Smith

2000

Mh Math

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A subsemigroup S of a completely regular semigroup Q is an order in Q if every element of Q can be written as a 5 b and as cd 5 where aY bY cY d P S and x 5 is the inverse of x P Q in a subgroup of Q. If only the ®rst condition holds and one insists also that a R b in Q, then S is said to be a straight left order in Q. This paper characterizes those semigroups that are straight left orders in completely regular semigroups. A consequence of this result, together with some technicalities concerning lifting of morphisms, is a description of orders in completely regular semigroups.2000 Mathematics Subject Classi®cation: 20 M 10

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Orders in completely regular semigroups

Cited by 3 publications

References 12 publications

On Orders in Normal Cryptogroups

On Orders in Normal Cryptogroups

Properties of GV-semigroups

Orders and Straight Left Orders in Completely Regular Semigroups

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