Research article

Intersectional soft gamma ideals of ordered gamma semigroups

  • Received: 23 December 2020 Accepted: 25 April 2021 Published: 30 April 2021
  • MSC : 08Axx, 08A72, 16Wxx

  • In contemporary mathematics, parameterization tool like soft set theory precisely tackle complex problems of economics and engineering. In this paper, we demonstrate a novel approach of soft set theory i.e., intersectional soft (int-soft) sets of an ordered $ \Gamma $ -semigroup $ S $ and develop int-soft left (resp. right) $ \Gamma $-ideals of $ S. $ Various classes like $ \Gamma $-regular, left $ \Gamma $-simple, right $ \Gamma $-simple and some semilattices of an ordered $ \Gamma $-semigroup $ S $ are characterize through int-soft left (resp. right) $ \Gamma $-ideals of $ S. $ Particularly, a $ \Gamma $-regular ordered $ \Gamma $-semigroup $ S $ is a left $ \Gamma $-simple if and only if every int-soft left $ \Gamma $-ideal $ f_{A} $ of $ S $ is a constant function. Also, $ S $ is a semilattice of left (resp. right) $ \Gamma $-simple $ \Gamma $-semigroup if and only if for every int-soft left (resp. right) $ \Gamma $-ideal $ f_{A} $ of $ S, $ $ f_{A}\left(a\right) = f_{A}\left(a\alpha a\right) $ and $ f_{A}\left(a\alpha b\right) = f_{A}\left(b\alpha a\right) $ for all $ a, b\in S $ and $ \alpha \in \Gamma $ hold.

    Citation: Faiz Muhammad Khan, Tian-Chuan Sun, Asghar Khan, Muhammad Junaid, Anwarud Din. Intersectional soft gamma ideals of ordered gamma semigroups[J]. AIMS Mathematics, 2021, 6(7): 7367-7385. doi: 10.3934/math.2021432

    Related Papers:

  • In contemporary mathematics, parameterization tool like soft set theory precisely tackle complex problems of economics and engineering. In this paper, we demonstrate a novel approach of soft set theory i.e., intersectional soft (int-soft) sets of an ordered $ \Gamma $ -semigroup $ S $ and develop int-soft left (resp. right) $ \Gamma $-ideals of $ S. $ Various classes like $ \Gamma $-regular, left $ \Gamma $-simple, right $ \Gamma $-simple and some semilattices of an ordered $ \Gamma $-semigroup $ S $ are characterize through int-soft left (resp. right) $ \Gamma $-ideals of $ S. $ Particularly, a $ \Gamma $-regular ordered $ \Gamma $-semigroup $ S $ is a left $ \Gamma $-simple if and only if every int-soft left $ \Gamma $-ideal $ f_{A} $ of $ S $ is a constant function. Also, $ S $ is a semilattice of left (resp. right) $ \Gamma $-simple $ \Gamma $-semigroup if and only if for every int-soft left (resp. right) $ \Gamma $-ideal $ f_{A} $ of $ S, $ $ f_{A}\left(a\right) = f_{A}\left(a\alpha a\right) $ and $ f_{A}\left(a\alpha b\right) = f_{A}\left(b\alpha a\right) $ for all $ a, b\in S $ and $ \alpha \in \Gamma $ hold.



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