Projection-primitive $ P $-Ehresmann semigroups

Shoufeng Wang; Shoufeng Wang

doi:10.3934/math.2021413

AIMS Mathematics

2021, Volume 6, Issue 7: 7044-7055. doi: 10.3934/math.2021413

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Research article

Projection-primitive $ P $-Ehresmann semigroups

Shoufeng Wang ^,

Department of Mathematics, Yunnan Normal University, Kunming, Yunnan, 650500, P. R. China

Received: 23 December 2020 Accepted: 23 April 2021 Published: 26 April 2021
MSC : 20M10, 20M50

$ P $-Ehresmann semigroups introduced by Jones are natural generalizations of Ehresmann semigroups. The aim of this paper is to introduce and describe projection-primitive $ P $-Ehresmann semigroups. More specifically, it is proved that a projection-primitive $ P $-Ehresmann semigroup is either isomorphic to a Rees matrix semigroup over a monoid with some natural conditions or a generalized category with zero adjoined.
- $ P $-Ehresmann semigroup,
- projection-primitive,
- generalized category
Citation: Shoufeng Wang. Projection-primitive $ P $-Ehresmann semigroups[J]. AIMS Mathematics, 2021, 6(7): 7044-7055. doi: 10.3934/math.2021413

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Abstract

$ P $-Ehresmann semigroups introduced by Jones are natural generalizations of Ehresmann semigroups. The aim of this paper is to introduce and describe projection-primitive $ P $-Ehresmann semigroups. More specifically, it is proved that a projection-primitive $ P $-Ehresmann semigroup is either isomorphic to a Rees matrix semigroup over a monoid with some natural conditions or a generalized category with zero adjoined.

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