Abstract
Let R be a commutative ring with nonzero identity and, be a multiplicatively closed subset. An ideal P of R with
is called an S-prime ideal if there exists an (fixed)
and whenver
for
then either
or
In this article, we construct a topology on the set SpecS(R) of all S-prime ideals of R which is generalization of prime spectrum of R. Also, we investigate the relations between algebraic properties of R and topological properties of SpecS(R) like compactness, connectedness and irreducibility.
Acknowledgement
The authors would like to thank the referee for his/her great efforts in proofreading the manuscript.