Principal ideal and Noetherian groups

S. Feigelstock and Z. Schlussel

Vol. 75 (1978), No. 1, 87–92

DOI: 10.2140/pjm.1978.75.87

Abstract

Let Π be a ring property. An additive group G is said to be an (associative) strongly Π-group if G is not nil, and if every (associative) ring R with additive group G such that R is not a zeroring has property Π. The (associative) strongly principal ideal groups, and the (associative) strongly Noetherian groups are classified for groups which are not torsion free. Some results are also obtained for the torsion free case.

Mathematical Subject Classification 2000

Primary: 20K10

Secondary: 16A66

Milestones

Received: 28 December 1976

Revised: 13 June 1977

Published: 1 March 1978