Soft intersection and soft union $k$-ideals of hemirings and their applications
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Abstract
The main aim of this paper is to discuss two different types of soft hemirings, soft intersection and soft union. We discuss applications and results related to soft intersection hemirings or soft intersection $k$-ideals and soft union hemirings or soft union $k$-ideals. The deep concept of $k$-closure, intersection and union of soft sets, $\wedge $-product and $\vee $-product among soft sets, upper $ \beta $-inclusion and lower $\beta $-inclusion of soft sets is discussed here. Many applications related to soft intersection-union sum and soft intersection-union product of sets are investigated in this paper. We characterize $k$-hemiregular hemirings by the soft intersection $k$-ideals and soft union $k$-ideals.
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