Strongly minimal modules over right distributive rings
Copyright policy )Strongly minimal modules over right distributive rings
Summary: For the case of right distributive rings, a description of strongly minimal right modules is given. In particular, we show that all strongly minimal faithful right modules are \(\Sigma\)-injective in this case. For a right distributive left Ore domain, a detailed description of strongly minimal indecomposable right modules is presented. We show that any strongly minimal faithful right module can be given the structure of a left module with respect to which it is strongly minimal and faithful.
Determinacy principles, strongly minimal faithful right modules, right distributive left Ore domains, strongly minimal right modules, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), right distributive rings, Applications of logic in associative algebras, Injective modules, self-injective associative rings, Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras), Divisibility, noncommutative UFDs, indecomposable right modules
Determinacy principles, strongly minimal faithful right modules, right distributive left Ore domains, strongly minimal right modules, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), right distributive rings, Applications of logic in associative algebras, Injective modules, self-injective associative rings, Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras), Divisibility, noncommutative UFDs, indecomposable right modules
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