(–1, 1) metabelian rings

Abstract

The structure of the set of all non- nilpotent (–1, 1) metabelian rings is studied. An additive basis of a free (–1, 1) metabelian ring is constructed. It is proved that any identity in a non- nilpotent 2, 3-torsion free (–1, 1) metabelian ring of degree greater than or equal to 6 is a consequence four defining identities of m where m is the metabelian (–1, 1) ring.

Keywords

• Non-nilpotent variety of metabelian (–1, 1) rings
• free metabelian (–1, 1) rings
• (–1, 1) rings