# 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

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topMridul 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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- [2] S. Chattopadhyay, Right Orthodox Γ-semigroup, Southeast Asian Bull. of Math 29 (2005), 23-30. Zbl1066.20066
- [3] J.M. Howie, An introduction to semigroup theory, Academic Press 1976.
- [4] W.R. Nico, On the regularity of semidirect products, J. Algebra 80 (1983), 29-36. Zbl0512.20043
- [5] T. Saito, Orthodox semidirect product and wreath products of semigroups, Semigroup Forum 38 (1989), 347-354. Zbl0669.20049
- [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] M.K. Sen and N.K Saha, On Γ-semigroup I, Bull. Cal. Math. Soc. 78 (1986), 181-186.
- [8] P.S. Venkatesan, Right(left) inverse semigroup, J. of Algebra (1974), 209-217. Zbl0301.20058
- [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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