ADS modules
نویسندگان
چکیده
We study the class of ADS rings and modules introduced by Fuchs [F]. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that RR is ADS must be either right self-injective or indecomposable as a right Rmodule. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.
منابع مشابه
On Ads-modules with the SIP
The class of ads modules with the SIP (briefly, $SA$-modules) is studied. Various conditions for a module to be $SA$-module are given. It is proved that for a quasi-continuous module $M$, $M$ is a UC-module if and only if $M$ is an $SA$-module. Also, it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...
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The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors ...
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