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Generalized lower and upper approximations in a ring. (English) Zbl 1192.16046

Summary: The concepts of set-valued homomorphism and strong set-valued homomorphism of a ring are introduced, and related properties are investigated. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximation of a ring, are provided. We also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by B. Davvaz [Inf. Sci. 164, No. 1-4, 147-163 (2004; Zbl 1072.16042)] in a ring and discuss some significant properties of them.

MSC:

16Y99 Generalizations
16W20 Automorphisms and endomorphisms

Citations:

Zbl 1072.16042
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