Toma Albu: The Osofsky-Smith Theorem in rings, modules, categories, and lattices, 371-387

Abstract:

In this survey paper we present various extensions of the renown Osofsky-Smith Theorem from Ring and Module Theory to modular lattices, Grothendieck categories, and module categories equipped with a hereditary torsion theory.

Key Words: Modular lattice, upper continuous lattice, complement, pseudo-complement, closed element, pseudo-complemented lattice, CS module, CC lattice, the Osofsky-Smith Theorem, the Latticial Osofsky-Smith Theorem, the Categorical Osofsky-Smith Theorem, the Relative Osofsky-Smith Theorem, hereditary torsion theory, Grothendieck category.

2010 Mathematics Subject Classification: Primary 06-02, 06C05, 16S90, 18E15; Secondary 06C99, 06B35, 16D80.