Quasi-injective modules withacc ordec on essential submodules
Copyright policy )Quasi-injective modules withacc ordec on essential submodules
It is shown that finitely generated modules with the properties given in the title are noetherian resp. artinian. Another result in the paper is that the endomorphism ring of a quasi-injective, quasi-projective module with acc on essential submodules is a ring direct sum of a left artinian ring and a von Neumann regular, left self-injective ring. Also, a new characterization of QF-rings is given: A left self-injective ring with acc on essential left or right ideals is a QF-ring. Recall that [in \textit{E. Armendariz}, Commun. Algebra 8, 299-308 (1980; Zbl 0444.16015)], QF- rings are characterized as left self-injective rings with dcc on essential left or right ideals.
- Institute of Mathematics Viet Nam
endomorphism ring, QF-rings, quasi-projective module with acc on essential submodules, Injective modules, self-injective associative rings, direct sum, Chain conditions on annihilators and summands: Goldie-type conditions, finitely generated modules, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), von Neumann regular, left self-injective ring, left artinian ring
endomorphism ring, QF-rings, quasi-projective module with acc on essential submodules, Injective modules, self-injective associative rings, direct sum, Chain conditions on annihilators and summands: Goldie-type conditions, finitely generated modules, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), von Neumann regular, left self-injective ring, left artinian ring
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