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- W2754847064 abstract "Abstract As a generalization of the class of inverse semigroups, the class of Ehresmann semigroups is introduced by Lawson and investigated by many authors extensively in the literature. In particular, Gomes and Gould construct a fundamental Ehresmann semigroup C E from a semilattice E which plays for Ehresmann semigroups the role that T E plays for inverse semigroups, where T E is the Munn semigroup of a semilattice E . From a varietal perspective, Ehresmann semigroups are derived from reduction of inverse semigroups. In this paper, from varietal perspective Ehresmann semigroups are extended to generalized Ehresmann semigroups derived instead from normal orthodox semigroups (i.e. regular semigroups whose idempotents form normal bands) with an inverse transversal. We present here a semigroup C ( I ,Λ, E ∘ ) from an admissible triple ( I , Λ, E ∘ ) that plays for generalized Ehresmann semigroups the role that C E from a semilattice E plays for Ehresmann semigroups. More precisely, we show that a semigroup is a fundamental generalized Ehresmann semigroup whose admissible triple is isomorphic to ( I , Λ, E ∘ ) if and only if it is (2,1,1,1)-isomorphic to a quasi - full (2,1,1,1)-subalgebra of C ( I ,Λ, E ∘ ) . Our results generalize and enrich some results of Fountain, Gomes and Gould on weakly E-hedges semigroups and Ehresmann semigroups." @default.
- W2754847064 created "2017-09-25" @default.
- W2754847064 creator A5082973627 @default.
- W2754847064 date "2017-09-06" @default.
- W2754847064 modified "2023-09-27" @default.
- W2754847064 title "On generalized Ehresmann semigroups" @default.
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- W2754847064 doi "https://doi.org/10.1515/math-2017-0091" @default.
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