LOCAL RINGS OF BOUNDED MODULE TYPE ARE ALMOST MAXIMAL VALUATION RINGS
نویسندگان
چکیده
منابع مشابه
Local rings of bounded module type are almost maximal valuation rings
It is shown that every commutative local ring of bounded module type is an almost maximal valuation ring. We say that an associative commutative unitary ring R is of bounded module type if there exists a positive integer n such that every finitely generated R-module is a direct sum of submodules generated by at most n elements. For instance, every Dedekind domain has bounded module type with bo...
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The aim of this paper is to generalize thenotion of pseudo-almost valuation domains to arbitrary commutative rings. It is shown that the classes of chained rings and pseudo-valuation rings are properly contained in the class of pseudo-almost valuation rings; also the class of pseudo-almost valuation rings is properly contained in the class of quasi-local rings with linearly ordere...
متن کاملCommutative Local Rings of bounded module type
Let R be a local ring of bounded module type. It is shown that R is an almost maximal valuation ring if there exists a non-maximal prime ideal J such that R/J is an almost maximal valuation domain. We deduce from this that R is almost maximal if one of the following conditions is satisfied: R is a Q-algebra of Krull dimension ≤ 1 or the maximal ideal of R is the union of all non-maximal prime i...
متن کاملAlmost valuation rings
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متن کاملpseudo-almost valuation rings
the aim of this paper is to generalize thenotion of pseudo-almost valuation domains to arbitrary commutative rings. it is shown that the classes of chained rings and pseudo-valuation rings are properly contained in the class of pseudo-almost valuation rings; also the class of pseudo-almost valuation rings is properly contained in the class of quasi-local rings with linearly ordere...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2005
ISSN: 0092-7872,1532-4125
DOI: 10.1081/agb-200064072