Trough Semiprime Ideals on Commutative Rings
Authors
S. B. Hosseini
 Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.
Abstract
Rough sets were originally proposed in the presence of an equivalence
relation. An equivalence relation is sometimes difficult to be obtained in
rearward problems due to the vagueness and incompleteness of human knowledge.
The purpose of this paper is to introduce and discuss the concept of
Trough semiprime ideal, Trough fuzzy semiprime ideal and Trough quotient
ideal in a commutative ring which are a generalization of rough set and approximation
theory. We compare relation between a rough ideal and a Trough
ideal and prove some theorems.
Keywords
 approximation space
 rough ideal
 semiprime ideal
 Trough set
 setvalued homomorphism
 Trough semiprime ideal
 Trough fuzzy ideal
 commutative ring.
MSC
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