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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 18, 2015

On Vn-semigroups

  • Ze Gu and Xilin Tang
From the journal Open Mathematics

Abstract

In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups in general. Therefore, the class of Vn-semigroups (n ≥ 2) does not form an e-variety. Finally, we obtain that a E-solid semigroup S is a V2-semigroup if and only if S is orthodox.

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Received: 2014-11-18
Accepted: 2015-12-3
Published Online: 2015-12-18

©2015 Gu and Tang

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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