Research ArticleNo Access

Isbell’s Zigzag theorem for permutative orthodox semigroups and clifford semigroups

Noor Alam

https://orcid.org/0000-0002-6961-7565

Department of Basic Sciences, Deanship of Preparatory Year, University of Ha’il, Ha’il-2440, K.S.A.

E-mail Address: alam.nooramu@gmail.com

Corresponding author.

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and

Noor Mohammad Khan

Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

E-mail Address: nm_khan123@yahoo.co.in

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https://doi.org/10.1142/S1793557122501431Cited by:0 (Source: Crossref)

Abstract

In this paper, we prove that the dominion of any full orthodox subsemigroup of a medial orthodox semigroup is described by the Isbell zigzag theorem in the category of medial orthodox semigroups. As a consequence, the dominions of any full completely regular subsemigroup of a medial completely regular semigroup as well as that of any full Clifford subsemigroup of a medial Clifford semigroup are also described by the Isbell zigzag theorem in the categories of all medial completely regular semigroups and of all medial Clifford semigroups, respectively.

Communicated by N. Gilbert

Keywords:

AMSC: 20M10, 20M17

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