Definability in the lattice of ring varieties

A. A. Iskander

Vol. 76 (1978), No. 1, 61–67

DOI: 10.2140/pjm.1978.76.61

Abstract

A variety of associative rings B immediately covers its subvariety A if every member of B outside A generates B. The variety {2x = 0,xy = 0} is the unique equationally complete variety with precisely two immediate covers in the lattice of all associative ring varieties. The variety of all Boolean rings is first order definable in the lattice of all associative ring varieties. So are the varieties defined by {2x = 0,xy − yx = 0} and {xy = 0}.

Mathematical Subject Classification

Primary: 08A15, 08A15

Milestones

Received: 22 June 1973

Revised: 3 October 1977

Published: 1 May 1978