ROUGH PRIME BI -IDEAL IN SEMIRINGS
Keywords:
PRELIMINARIESAbstract
Semiring which are common generalization of also relative ring and distributive lattice are found in abundance around us Vandiver[ 22] introduced semirings. Iseki[6] introduced the notion of ideals in semirings. Shabi and Kanwal[ 16] introduced prime bi-ideals in semigroups. Bashir et.al.,[1] introduced prime bi-ideals in semirings. The notion of rough sets was introduced by Pawlak in his papers [11-14]. Rough set theory is an extension of set theory, in which a subset of a universe is described by a pair of ordinary sets called the lower and upper approximations. Rough sets are a suitable mathematical model of vague concepts, i.e., concepts without sharp boundaries. It soon invoked a natural question concerning possible connection between rough sets and algebraic systems. The application of rough set theory in the algebraic structure was studied by many others such as Z.Bonikowaski[3], J.Pomykala[15], Y.B.Jun[8], T.Iwinski[7]. The notion of rough ideals was introduced by N.Kuroki[9]. Biswas and Nanda[2] introduced rough groups and subgroups.
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