t-Splitting sets in integral domains
نویسندگان
چکیده
منابع مشابه
T-splitting Multiplicative Sets of Ideals in Integral Domains
Let D be an integral domain. We study those multiplicative sets of ideals S of D with the property that every nonzero principal ideal dD of D can be written as dD = (AB)t with A, B ideals of D such that A contains some ideal in S and (C + B)t = D for each C ∈ S . Let D be an integral domain with quotient Þeld K and let F (D) be the set of nonzero fractional ideals of D. Clearly, for A ∈ F (D), ...
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Let D be an integral domain. A multiplicative set S of D is an almost splitting set if for each 0 6= d ∈ D, there exists an n = n(d) with dn = st where s ∈ S and t is v-coprime to each element of S. An integral domain D is an almost GCD (AGCD) domain if for every x, y ∈ D, there exists a positive integer n = n(x, y) such that xnD ∩ ynD is a principal ideal. We prove that the polynomial ring D[X...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2003.07.001