Extensions of fuzzy subrings and fuzzy ideals

Abstract In this paper we give necessary and sufficient conditions for a fuzzy subring or a fuzzy ideal A of a commutative ring R to be extended to one A e of a commutative ring S containing R as a subring such that A and A e have the same image. One of the applications of these results gives a criterion for a fuzzy subring of an integral domain R to be extendable to a fuzzy subfield of the quotient field of R .