Congruences on bands of π-groups

Sunil K. Maity

Discussiones Mathematicae - General Algebra and Applications (2013)

  • Volume: 33, Issue: 1, page 5-11
  • ISSN: 1509-9415

Abstract

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A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.

How to cite

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Sunil K. Maity. "Congruences on bands of π-groups." Discussiones Mathematicae - General Algebra and Applications 33.1 (2013): 5-11. <http://eudml.org/doc/270749>.

@article{SunilK2013,
abstract = {A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.},
author = {Sunil K. Maity},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {group congruence; completely regular semigroup congruence; bands of groups; group congruences; completely regular semigroups; regular semigroup congruences},
language = {eng},
number = {1},
pages = {5-11},
title = {Congruences on bands of π-groups},
url = {http://eudml.org/doc/270749},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Sunil K. Maity
TI - Congruences on bands of π-groups
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2013
VL - 33
IS - 1
SP - 5
EP - 11
AB - A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.
LA - eng
KW - group congruence; completely regular semigroup congruence; bands of groups; group congruences; completely regular semigroups; regular semigroup congruences
UR - http://eudml.org/doc/270749
ER -

References

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  1. [1] S. Bogdanovic, Semigroups with a System of Subsemigroups (Novi Sad, 1985). Zbl0569.20049
  2. [2] S. Bogdanovic and M. Ciric, Retractive Nil-extensions of Bands of Groups, Facta Universitatis 8 (1993) 11-20. Zbl0831.20073
  3. [3] T.E. Hall, On Regular Semigroups, J. Algebra 24 (1973) 1-24. doi: 10.1016/0021-8693(73)90150-6. 
  4. [4] J.M. Howie, Introduction to the theory of semigroups (Academic Press, 1976). 
  5. [5] D.R. LaTorre, Group Congruences on Regular semigroups, Semigroup Forum 24 (1982) 327-340. doi: 10.1007/BF02572776. Zbl0487.20039
  6. [6] P.M. Edwards, Eventually Regular Semigroups, Bull. Austral. Math. Soc 28 (1982) 23-38. doi: 10.1017/S0004972700026095. Zbl0511.20044
  7. [7] W.D. Munn, Pseudo-inverses in Semigroups, Proc. Camb. Phil. Soc. 57 (1961) 247-250. doi: 10.1017/S0305004100035143. Zbl0228.20057
  8. [8] M. Petrich, Regular Semigroups which are subdirect products of a band and a semilattice of groups, Glasgow Math. J. 14 (1973) 27-49. doi: 10.1017/S0017089500001701. Zbl0257.20055
  9. [9] M. Petrich and N.R. Reilly, Completely Regular Semigroups (Wiley, New York, 1999). Zbl0967.20034
  10. [10] S.H. Rao and P. Lakshmi, Group Congruences on Eventually Regular Semigroups, J. Austral. Math. Soc. (Series A) 45 (1988) 320-325. doi: 10.1017/S1446788700031025. Zbl0665.20032
  11. [11] S. Sattayaporn, The Least Group Congruences On Eventually Regular Semigroups, International Journal of Algebra 4 (2010) 327-334. Zbl1208.20051
  12. [12] J. Zeleznekow, Regular semirings, Semigroup Forum 23 (1981) 119-136. doi: 10.1007/BF02676640. 

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