On V n -semigroups

Ze Gu; Xilin Tang

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 101-116
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ze Gu, and Xilin Tang. " On V n -semigroups ." Open Mathematics 13.1 (2015): 101-116. <http://eudml.org/doc/276433>.

@article{ZeGu2015,
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.},
author = {Ze Gu, Xilin Tang},
journal = {Open Mathematics},
keywords = {Orthodox semigroups; V n-semigroups; V 2-semigroups; E-solid semigroup; e-variety; varieties of regular semigroups; regular unary semigroups; word problem; inverse transversals; semilattice transversals; free bands; free IST-bands; IST-varieties},
language = {eng},
number = {1},
pages = {101-116},
title = { On V n -semigroups },
url = {http://eudml.org/doc/276433},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Ze Gu
AU - Xilin Tang
TI - On V n -semigroups
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 101
EP - 116
AB - 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.
LA - eng
KW - Orthodox semigroups; V n-semigroups; V 2-semigroups; E-solid semigroup; e-variety; varieties of regular semigroups; regular unary semigroups; word problem; inverse transversals; semilattice transversals; free bands; free IST-bands; IST-varieties
UR - http://eudml.org/doc/276433
ER -

References

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  11. [11] Tang, X.L., Free orthodox semigroups and free bands with inverse transversals, Science China Mathematics, 2010, 53(11), 3015- 3026 [WoS] Zbl1219.20039
  12. [12] Tang, X.L., Gu, Z., Words on free bands with inverse transversals, Semigroup Forum, 2015, 91, 101-116 [WoS] Zbl1341.20061
  13. [13] Wang, L.M., On congruence lattices of regular semigroups with Q-inverse transversals, Semigroup Forum, 1995, 50, 141-160 [Crossref] Zbl0828.20053
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  15. [15] Hall, T.E., Congruences and Green’s relations on regular semigroups, Glasgow Mathematical Journal, 1972, 13(02), 167-175 [Crossref] Zbl0257.20057

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