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In this paper, we intend to study a connection between rough sets and lattice theory. We introduce the concepts of upper and lower rough ideals (filters) in a lattice. Then, we offer some of their properties with regard to prime ideals (filters), the set of all fixed points, compact elements, and homomorphisms. 2012 Elsevier Inc. All rights reserved.
Let C(X) be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of C(X). The intersection of essential weak ideal in C(X) is also studied.
In this paper, we introduce the notion of fuzzy primary subact and study some important properties. Finally, we show that a non-constant fuzzy subact μ of S-act A is a fuzzy P-primary subact of A if and only if for every fuzzy point a of A and fuzzy point S of S, if a s β α ∈μ and a ∈μ / , then S∈P and if S∈P, then there is an n∈N such that n A (s ) α χ ⊆… (More)
Let C(L) be the ring of real-valued continuous functions on a frame L. In this paper, strongly fixed ideals and characterization of maximal ideals of C(L) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed… (More)