BROWN-McCOY RADICALS FOR GENERAL NEAR-RINGS

Abstract

Two possible ways of extending the Brown-McCoy radical to non-0-symmetric near-rings are discussed. If a Kurosh-Amitsur semisimple class S_o in the class N_o of 0-symmetric near-rings satisfies a certain condition on local units, then S_o is a Kurosh-Amitsur semisimple class also in the class N of all near-rings. So the subdirect closure of the class of simple 0-symmetric near-rings with identity is a Kurosh-Amitsur semisimple class in N with non-hereditary radical class. The Hoehnke radical eE determined by the class of simple near-rings with identity is not idempotent, though for every N ε N the radical eE (N) is the unique largest G-regular ideal of N. In both cases the radical classes are hereditary with respect to invariant ideals.

Mathematics Subject Classification (2000):

• Primary 16Y30
• Secondary 16N99

Key words:

• Non-0-symmetric near-ring
• Brown-McCoy radical