Cofinitely generated and cofinitely related modules
Copyright policy )Cofinitely generated and cofinitely related modules
P. VAMOS [11] has defned and studied 'finitely embedded modules' as the dual of 'finitely generated modules'. JANS [4] called them as co finitely generated modules and defined a right co-noetherian ring as dual to a right noetherian ring and investigated their properties. In this paper, we obtain a categorical justification for finitely embedded modules to be the dual of finitely generated modules, and derive some more properties of cofinitely generated modules. Then we define, as dual to 'a finitely related module', 'a cofinitely related module' and derive its properties. Throughout this paper, by a ring R we mean an associative ring with identity
Category-theoretic methods and results in associative algebras (except as in 16D90), finitely generated modules, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), finitely embedded modules, Other classes of modules and ideals in associative algebras, cofinitely generated modules
Category-theoretic methods and results in associative algebras (except as in 16D90), finitely generated modules, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), finitely embedded modules, Other classes of modules and ideals in associative algebras, cofinitely generated modules
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