IJPAM: Volume 86, No. 6 (2013)

$\Gamma$-SEMIGROUPS WITH LOCAL UNITS AND
MORITA EQUIVALENCE OF SEMIGROUPS
WITH LOCAL UNITS

Sugato Gupta$^1$, Sujit Kumar Sardar$^2$
$^{1,2}$Department of Mathematics
Jadavpur University
Kolkata, 700032, INDIA


Abstract. In this paper we define local units for $\Gamma$-semigroups and show that two semigroups $L$ and $R$ with local units are Morita equivalent if and only if there exists a $\Gamma$-semigroup $A$ with local units whose operator semigroups are isomorphic to $L$ and $R$. We apply this result to study some interplays between operator semigroups of $\Gamma$-semigroups with local units by using Morita theories for semigroups.

Received: May 9, 2013

AMS Subject Classification: 20M30, 20M50

Key Words and Phrases: $\Gamma$-semigroup, Morita equivalence

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DOI: 10.12732/ijpam.v86i6.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 6