Vol. 66, No. 2, 1976

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ISSN: 0030-8730
Rings whose additive subgroups are subrings

John Dacey O’Neill

Vol. 66 (1976), No. 2, 509–522
Abstract

In this paper the class (subclass) of associative rings whose additive subgroups are subrings (ideals) is completely characterized by defining relations. An exact description is also given of those rings in these classes which are commutative, regular, Artinian, Noetherian, or with identity. The only integral domains in either class are the ring of integers Z and Z∕(p) for prime p.

Mathematical Subject Classification
Primary: 16A48, 16A48
Milestones
Received: 23 February 1976
Published: 1 October 1976
Authors
John Dacey O’Neill