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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 80
   School of Mathematics
  Title: Rough sets in a fundamental ring
  Author(s): B. Davvaz
  Status: Published
  Journal: Bull. Iranian Math. Soc.
  No.: 2
  Vol.: 24
  Year: 1998
  Pages: 49-61
  Supported by: IPM
  Abstract:
The largest class of multivalued systems satisfying ring-like axioms is the Hv-ring. Let R be an Hv-ring and γ* be the smallest equivalence relation on R such that the quotient R*, the set of all equivalence classes, is a ring. In this paper we consider the relation γ* defined on R and define the lower and upper approximations of a subset A of R with respect to γ*. We interprete the lower and upper approximations as subsets of the ring R* and we prove some results in this connection. In particular, we show that if A is an Hv-ideal of R then upper approximation of A is an ideal of R*.

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