Affiliations: Department of Mathematics, Hubei University for Nationalities, Enshi, China
Note: [] Corresponding author. Jianming Zhan, Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province 445000, China. Tel.: +86 718 8437732. E-mails: zjmhbmy@126.com (X. Ma); zhanjianming@hotmail.com (J. Zhan).
Abstract: The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of (M,N)-SI-hemirings ((M,N)-SI-h-ideals) of hemirings, which are generalizations of SI-hemirings (SI-h-ideals). By soft union-intersection sums (products), some related properties are discussed. Special attention is paid to quotient soft hemirings. Finally, we investigate some characterizations of h-hemiregular hemirings by means of (M,N)-SI-h-ideals.
Keywords: Soft set, soft union-intersection sum (product), (M,N)-SI-hemiring((M,N)-SI-h-ideal), h-hemiregular hemiring
