In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility andâ€¦ (More)

The notion of k-regularity in a semiring generalizes the notion of a regular ring introduced by J. Von Neumaan [15]. In semiring theory, the notion of k-regularity was extensively studied by Sen and Bhuniya [17]. In this paper, we study the concept of k-regularities of a semiring in fuzzy setting and characterize some k-regularities of semirings by usingâ€¦ (More)

Abstract. The interval-valued prime fuzzy ideals (in brevity, the iv. prime fuzzy ideals) of a semigroup have been recently studied by Kar, Sarkar and Shum [18]. As a continued study of i-v fuzzy ideals, we are going to investigate the properties of i-v fuzzy quasi-ideal and i-v fuzzy bi-ideal of a semiring and then we characterize the regularity andâ€¦ (More)

We obtain expressions for sums of the form âˆ‘m j=0(âˆ’1) j ( m j ) ( n+j j ) and deduce, for an even integer d â‰¥ 0 and m = n > d/2, that this sum is 0 or 1 2 according as to whether d > 0 or not. Further, we prove for even d > 0 that âˆ‘d l=1 clâˆ’1 (âˆ’1) ( n l ) l! (l+1) ( 2n l+1 ) = 0 where cr = 1 r! âˆ‘rs=0(âˆ’1)s(rs)(r âˆ’ s + 1)dâˆ’1. Similarly, we show when d > 0 isâ€¦ (More)