Sudipta Purkait

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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 and(More)
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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 using(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 and(More)
We obtain expressions for sums of the form ∑m j=0(−1) j ( m j ) ( n+j j ) and deduce, for an even integer d ≥ 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 ∑d l=1 cl−1 (−1) ( n l ) l! (l+1) ( 2n l+1 ) = 0 where cr = 1 r! ∑rs=0(−1)s(rs)(r − s + 1)d−1. Similarly, we show when d > 0 is(More)
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