On V n -semigroups
Ze Gu ; Xilin Tang
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:276433 
@article{bwmeta1.element.doi-10_1515_math-2015-0085,
     author = {Ze Gu and Xilin Tang},
     title = {
      On V
      n
      -semigroups
    },
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     zbl = {1341.20061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0085}
}

Ze Gu; Xilin Tang. 
      On V
      n
      -semigroups
    . Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0085/

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