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The Scientific World Journal
Volume 2014, Article ID 136424, 7 pages
http://dx.doi.org/10.1155/2014/136424
Research Article

Ideal Theory in Semigroups Based on Intersectional Soft Sets

1Department of Mathematics, Jeju National University, Jeju 690-756, Republic of Korea
2Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea
3Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 18 March 2014; Accepted 22 May 2014; Published 23 June 2014

Academic Editor: Feng Feng

Copyright © 2014 Seok Zun Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discussed. We prove that the soft intersection of int-soft left (resp., right) ideals (resp., int-soft semigroups) is also int-soft left (resp., right) ideals (resp., int-soft semigroups). The concept of int-soft quasi-ideals is also introduced, and characterization of a regular semigroup is discussed.