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On Generalized Ideals of Left Almost Semigroups

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2016

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Abstract (2. Language): 
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 (le f t) ideal of S, then either RmLn = {0} or RmLn is 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.
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REFERENCES

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