Wreath product of a semigroup and a Γ-semigroup

• Autorzy: Mridul K. Sen , Sumanta Chattopadhyay
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 20M17: Regular semigroups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 161-178

Daty

wydano

2008

otrzymano

2007-08-10

poprawiono

2007-09-14

Twórcy

autor

Mridul K. Sen

• Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata-700019, India

autor

Sumanta Chattopadhyay

• Sri Ramkrishna Sarada Vidyamahapitha Kamarpukur, Hooghly-712612, West Bengal, India

Bibliografia

• [1] S. Chattopadhyay, Right Inverse Γ-semigroup, Bull. Cal. Math. Soc. 93 (2001), 435-442.
• [2] S. Chattopadhyay, Right Orthodox Γ-semigroup, Southeast Asian Bull. of Math 29 (2005), 23-30.
• [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.
• [5] T. Saito, Orthodox semidirect product and wreath products of semigroups, Semigroup Forum 38 (1989), 347-354.
• [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.
• [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.
• [9] R. Zhang, A Note on Orthodox Semidirect Products and Wreath Products of Monoids, Semigroup Forum 58 (1999), 262-266.

Identyfikatory

DOI

10.7151/dmgaa.1141