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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (54), 2007/

On natural and conatural sets of left ideals of a ring.

Authors: Caşu Alexei

Abstract

The natural and conatural sets of left ideals of a ring R are defined by analogy with natural and conatural classes of left R-modules [4, 5]. Some characterizations and properties of such sets are indicated. The lattices of natural sets R-Nat and of conatural sets R-Conat of R are treated as skeletons of more wide lattices of closed and coclosed sets. In particular, R-Nat and R-Conat are boolean lattices.

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