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MCD-Domain of type A+x B[x] and A+xB[[x]] | ||
| Tikrit Journal of Pure Science | ||
| Article 1, Volume 13, Issue 1, 2008, Pages 13-15 | ||
| Author | ||
| Mahera Rabee Q | ||
| 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. | ||
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