Congruence networks for completely simple semigroups

Petrich, Mario

doi:10.1017/s1446788700034868

Cited by 6 publications

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References 7 publications

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“…In [4], we performed a similar analysis for the operators K, T , k, t. In this case, the corresponding network is finite and of quite simple structure. We may order these (two-sided) networks by letting u ≤ v if ρu ⊆ ρv for all ρ ∈ C(S).…”

Section: Introductionmentioning

confidence: 99%

The structure of two-sided networks for completely simple semigroups

Petrich¹

2002

Publ. Math. Debrecen

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As a byproduct of the kernel-trace approach to congruences on regular semigroups S we have the operators Γ = {T l , K, T r , t l , k, t r } induced by the classes of the left trace, kernel and right trace relations via their upper and lower ends. The semigroup generated by these operators forms the two-sided network of S.For S a Rees matrix semigroup with a normalized sandwich matrix, the two-sided network Ω was characterized in a previous paper by the author in terms of generators and relations. The theme of this paper is the structure of Ω. After isolating the right zeros of Ω, consisting of constant operators, we find the structure of the rest by means of certain triples. These triples resemble those of a Rees matrix semigroup and indeed a part of Ω can be embedded into such a semigroup. Other structural features of Ω are studied together with a special case.

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Section: Introductionmentioning

confidence: 99%