“School of Mathematics”
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Paper IPM / M / 80  


Abstract:  
The largest class of multivalued systems satisfying ringlike
axioms is the H_{v}ring. Let R be an H_{v}ring and γ^{*}
be the smallest equivalence relation on R such that the quotient
R/γ^{*}, 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/γ^{*} and we prove
some results in this connection. In particular, we show that if
A is an H_{v}ideal of R then upper approximation of A is an
ideal of R/γ^{*}.
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