Distributive rings
Copyright policy )Distributive rings
Let R be an associative ring with identity. R is said to be right distributive - or right arithmetical - (resp. right chain) if the lattice of right ideals is distributive (resp. is a chain). The main result of this paper is the following: R is a noetherian right distributive ring if and only if R is isomorphic to a finite direct product of artinian right chain rings and hereditary noetherian duo domains.
Noetherian rings and modules (associative rings and algebras), Associative rings and algebras with additional structure, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), noetherian right distributive ring, Artinian rings and modules (associative rings and algebras), hereditary Noetherian duo domains, Noetherian right distributive rings, direct product of artinian right chain rings, lattice of right ideals, hereditary noetherian duo domains, Modules, bimodules and ideals in associative algebras, direct product of Artinian right chain rings
Noetherian rings and modules (associative rings and algebras), Associative rings and algebras with additional structure, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), noetherian right distributive ring, Artinian rings and modules (associative rings and algebras), hereditary Noetherian duo domains, Noetherian right distributive rings, direct product of artinian right chain rings, lattice of right ideals, hereditary noetherian duo domains, Modules, bimodules and ideals in associative algebras, direct product of Artinian right chain rings
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