Neat rings
A ring is clean if every element is a sum of a unit and an idempotent. A ring is neat if every proper factor of it is clean. The paper has several results on neat rings: (1) a collection of several equivalent conditions for a commutative ring to be clean. (2) classification of neatness for some classes of rings: (a) rings over which every finitely generated module is a direct sum of cyclics, (b) Bézout domains (in terms of their group of divisibility); (3) Other examples of neat rings: (a) every h-local domain; (b) every domain with Krull dimension. Besides these, the last two sections of the paper contain generalizations on rigid extension of lattice-ordered abelian groups and relating properties of the additive group of continuous functions of a topological space to its topology. These two sections are independent of the rest of the paper.
rigid extension of lattice-ordered groups
scientific article; zbMATH DE number 5016243
scientific article