### On (m,n)-ideals of left almost semigroups

#### Abstract

In this paper, we study (m,n)-ideals of an LA -semigroup in detail. We characterize (0,2)-ideals of an LA -semigroup S and prove that A is a (0,2)-ideal of S if and only if A is a left ideal of some left ideal of S. We also show that an LA -semigroup S is 0-(0,2)-bisimple if and only if S is right 0-simple. Furthermore we study 0-minimal (m,n)-ideals in an LA -semigroup S and prove that if R (L) is a 0-minimal right (left) ideal of S, then either RmLn= {0} or RmLnis a 0-minimal (m,n)-ideal of S for m,n ≥ 3. Finally we discuss (m,n)-ideals in an (m,n)-regular LA -semigroup S and show that S is (0,1)-regular if and only if L = SL where L is a (0,1)-ideal of S.

**Published:**2014-07-22

**How to Cite this Article:**Faisal Yousafzai, Waqar Khan, Wenbin Guo, Madad Khan, On (m,n)-ideals of left almost semigroups, J. Semigroup Theory Appl., 2014 (2014), Article ID 1 Copyright © 2014 Faisal Yousafzai, Waqar Khan, Wenbin Guo, Madad Khan. 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.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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