IJPAM: Volume 87, No. 6 (2013)

$0$-SIMPLE AND SOFT $M$-SEMIGROUPS

S. Vijayabalaji$^1$, V. Shakila$^2$
$^{1,2}$Department of Mathematics
University College of Engineering Panruti
Pantruti, 607 106, Tamilnadu, INDIA


Abstract. Motivated by the theory of $0$- simple semigroup and $M$- semigroup, in this paper we introduce the notion of $0$- simple $M$- semigroup. We also focus our research towards soft set theory and introduce the notion of soft $M$- semigroup and provide some results on it. In a $0$- simple $M$- semigroup, we prove that $0$- minimal ideal is a $0$- simple $M$- semigroup and in soft setting, we prove that the union of the two soft $M$- semigroups is also a soft $M$- semigroup with the condition that the intersection of the subsets are empty. Also we justify that the Cartesian product of the two soft $M$- semigroups is also a soft $M$- semigroup.

Received: September 6, 2013

AMS Subject Classification: 20M10, 20M99

Key Words and Phrases: $M$- semigroup, soft sets, $0$- simple, soft $M$- semigroup, $0$- simple soft $M$- semigroup

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DOI: 10.12732/ijpam.v87i6.3 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: 87
Issue: 6