# On generalized Ehresmann semigroups

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1132-1147
- ISSN: 2391-5455

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topShoufeng Wang. "On generalized Ehresmann semigroups." Open Mathematics 15.1 (2017): 1132-1147. <http://eudml.org/doc/288299>.

@article{ShoufengWang2017,

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 CE from a semilattice E which plays for Ehresmann semigroups the role that TE plays for inverse semigroups, where TE 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 CE 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.},

author = {Shoufeng Wang},

journal = {Open Mathematics},

keywords = {Generalized Ehresmann semigroup; Fundamental semigroup; Fundamental representation},

language = {eng},

number = {1},

pages = {1132-1147},

title = {On generalized Ehresmann semigroups},

url = {http://eudml.org/doc/288299},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Shoufeng Wang

TI - On generalized Ehresmann semigroups

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1132

EP - 1147

AB - 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 CE from a semilattice E which plays for Ehresmann semigroups the role that TE plays for inverse semigroups, where TE 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 CE 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.

LA - eng

KW - Generalized Ehresmann semigroup; Fundamental semigroup; Fundamental representation

UR - http://eudml.org/doc/288299

ER -

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