MCD-Domain of type A+x B[x] and A+xB[[x]]

Abstract

In this paper we study MCD-Domain of type A+xB[x] and A+xB[[x]]. Let R be a commutative Ring with unity and S be a subset of R. The set of all nonzero common divisors of the elements in S by CDR(S). An element m in CDR(S) is called a maximal common divisor (for short an MCD) of S if m is associated with any element in CDR(S) which is divisible by m. A domain R is called MCD-Domain if every finite set of nonzero elements in R has an MCD.In corollary (III) and corollary (IIII) we shall given a new proof of [2,Theorem 1.1] , and see also [5, corollary 1.5] and for its power series analogue.