Wreath product of a semigroup and a Γ-semigroup

Mridul K. Sen; Sumanta Chattopadhyay

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 2, page 161-178
  • ISSN: 1509-9415

Abstract

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Let S = {a,b,c,...} and Γ = {α,β,γ,...} be two nonempty sets. S is called a Γ -semigroup if aαb ∈ S, for all α ∈ Γ and a,b ∈ S and (aαb)βc = aα(bβc), for all a,b,c ∈ S and for all α,β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γ-semigroup and investigate some interesting properties of this product.

How to cite

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Mridul K. Sen, and Sumanta Chattopadhyay. "Wreath product of a semigroup and a Γ-semigroup." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 161-178. <http://eudml.org/doc/276937>.

@article{MridulK2008,
abstract = {Let S = \{a,b,c,...\} and Γ = \{α,β,γ,...\} be two nonempty sets. S is called a Γ -semigroup if aαb ∈ S, for all α ∈ Γ and a,b ∈ S and (aαb)βc = aα(bβc), for all a,b,c ∈ S and for all α,β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γ-semigroup and investigate some interesting properties of this product.},
author = {Mridul K. Sen, Sumanta Chattopadhyay},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {semigroup; Γ-semigroup; orthodox semigroup; right(left) orthodox Γ-semigroup; right(left) inverse semigroup; right(left) inverse Γ-semigroup; right(left)α-unity; Γ-group; semidirect product; wreath product; -semigroups; wreath products; semidirect products},
language = {eng},
number = {2},
pages = {161-178},
title = {Wreath product of a semigroup and a Γ-semigroup},
url = {http://eudml.org/doc/276937},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Mridul K. Sen
AU - Sumanta Chattopadhyay
TI - Wreath product of a semigroup and a Γ-semigroup
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 2
SP - 161
EP - 178
AB - Let S = {a,b,c,...} and Γ = {α,β,γ,...} be two nonempty sets. S is called a Γ -semigroup if aαb ∈ S, for all α ∈ Γ and a,b ∈ S and (aαb)βc = aα(bβc), for all a,b,c ∈ S and for all α,β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γ-semigroup and investigate some interesting properties of this product.
LA - eng
KW - semigroup; Γ-semigroup; orthodox semigroup; right(left) orthodox Γ-semigroup; right(left) inverse semigroup; right(left) inverse Γ-semigroup; right(left)α-unity; Γ-group; semidirect product; wreath product; -semigroups; wreath products; semidirect products
UR - http://eudml.org/doc/276937
ER -

References

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  1. [1] S. Chattopadhyay, Right Inverse Γ-semigroup, Bull. Cal. Math. Soc. 93 (2001), 435-442. Zbl1002.20042
  2. [2] S. Chattopadhyay, Right Orthodox Γ-semigroup, Southeast Asian Bull. of Math 29 (2005), 23-30. Zbl1066.20066
  3. [3] J.M. Howie, An introduction to semigroup theory, Academic Press 1976. 
  4. [4] W.R. Nico, On the regularity of semidirect products, J. Algebra 80 (1983), 29-36. Zbl0512.20043
  5. [5] T. Saito, Orthodox semidirect product and wreath products of semigroups, Semigroup Forum 38 (1989), 347-354. Zbl0669.20049
  6. [6] M.K. Sen and S. Chattopadhyay, Semidirect Product of a Semigroup and a Γ-semigroup, East-West J. of Math. 6 (2) (2004), 131-138. Zbl1098.20052
  7. [7] M.K. Sen and N.K Saha, On Γ-semigroup I, Bull. Cal. Math. Soc. 78 (1986), 181-186. 
  8. [8] P.S. Venkatesan, Right(left) inverse semigroup, J. of Algebra (1974), 209-217. Zbl0301.20058
  9. [9] R. Zhang, A Note on Orthodox Semidirect Products and Wreath Products of Monoids, Semigroup Forum 58 (1999), 262-266. Zbl0926.20042

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