Mathematics Commons^™

A Note On Clean Abelian Groups, Brendan Goldsmith, P. Vamos

Articles

Nicholson defined a ring to be clean if every element is the sum of a unit and an idempotent. A module is clean if its endomorphism algebra is clean. We show that torsion-complete Abelian p-groups are clean and characterize the clean groups among the class of totally projective p-groups. An example is given of a clean p-group which is neither totally projective nor torsion- complete