منابع مشابه
Injective Modules and Fp-injective Modules over Valuation Rings
It is shown that each almost maximal valuation ring R, such that every indecomposable injective R-module is countably generated, satisfies the following condition (C): each fp-injective R-module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring R that satisfies this condition (C) is almost maximal. The converse holds if Spec(R) is countable....
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محور اصلی این پایان نامه، r- مدولهای a – انژکتیو می باشد که آنها را به عنوان یک تعمیم از مدول های انژکتیو معرفی می کنیم. در ابتدا مدول های انژکتیو را معرفی کرده، سپس برخی نتایج مهم وشناخته شده مدول های انژکتیو را به مدول های a – انژکتیو تعمیم می دهیم. در ادامه رابطه بین مدول های a – انژکتیو و حلقه های نوتری را بررسی می کنیم. پس هدف کلی این پایان نامه این است که با بررسی انژکتیو بودن ایده آله...
15 صفحه اولLocalization of Injective Modules over Valuation Rings
It is proved that EJ is injective if E is an injective module over a valuation ring R, for each prime ideal J 6= Z. Moreover, if E or Z is flat, then EZ is injective too. It follows that localizations of injective modules over h-local Prüfer domains are injective too. If S is a multiplicative subset of a noetherian ring R, it is well known that SE is injective for each injective R-module E. The...
متن کاملLocalization of injective modules over arithmetical rings
It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P , RP is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreove...
متن کاملTorsionfree Dimension of Modules and Self-injective Dimension of Rings
Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...
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ژورنال
عنوان ژورنال: Journal of Al-Qadisiyah for computer science and mathematics
سال: 2017
ISSN: 2521-3504,2074-0204
DOI: 10.29304/jqcm.2017.9.2.296