منابع مشابه
Commutative 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 کاملLocal 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...
متن کاملA class of Artinian local rings of homogeneous type
Let $I$ be an ideal in a regular local ring $(R,n)$, we will find bounds on the first and the last Betti numbers of $(A,m)=(R/I,n/I)$. if $A$ is an Artinian ring of the embedding codimension $h$, $I$ has the initial degree $t$ and $mu(m^t)=1$, we call $A$ a {it $t-$extended stretched local ring}. This class of local rings is a natural generalization of the class of stretched ...
متن کاملساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings
فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...
Localization at prime ideals in bounded rings
In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2005
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-004-8319-5