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Characterizations of Hemirings via (M, N)-SIh-bi-ideals and (M, N)-SIh-quasi-ideals
Jianming Zhan and Bin Yu

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. We introduce the concepts of (M, N)-SI-h-bi-ideals and (M, N)-SI-h-quasi-ideals of hemirings, where M, N are any two sets with ∅ ⊆ MNU. The relationships between these kinds of soft intersection (M, N)-hideals are established. Finally, some characterizations of h-hemiregular, h-intra-hemiregular hemirings and h-qausi-hemiregular hemirings are investigated by these kinds of (M, N)-SI-h-ideals, (M, N)-SI-h-biideals and (M, N)-SI-h-quasi-ideals.

Keywords: Soft set; (M, N)-SI-h-ideal; (M, N)-SI-h-bi-ideal; (M, N)-SI-h-quasi-ideal; (h-hemiregular, h-intra-hemiregular, h-quasi-hemiregular) hemiring.

2010 Mathematics Subject Classification: 16Y60; 13E05; 16Y99.

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