Maximal Right Nearring of Quotients and Semigroup Generalized Polynomial Identity

Abstract

In the present paper, we study the maximal right nearring of quotients of 3-semiprime nearrings. We establish its existence by an explicit construction and give an axiomatic description. We show that the operation of taking the maximal right nearring of quotients is idempotent. Further, we show that the maximal right nearring of quotients of a 3-prime nearring N with a minimal left N-subgroup is a centralizer nearring determined by some fixed point free group of automorphisms. Finally, we describe equiprime nearrings with nontrivial multilinear semigroup generalized polynomial identities. They are the equiprime nearrings whose maximal right nearring of quotients are the centralizer nearrings determined by commutative fixed point free groups of automorphisms.