The use of Computers in Near-Ring Theory

Abstract

We give a survey of our use of computers in near-ring theory. 1. THE PROBLEMS In this section we want to state some problems in near-ring theory, and how computer algebra can be used to attack those. Our notation concerning near-rings follows (13). (1) Given a set of mappings on a group, compute the near-ring generated by these mappings. Finding the near-rings l( G),E(G),A(G) falls into this category ofques­ tions. (2) Given a group, compute its (unary) polynomial functions .Polynomial functions on groups have received special interest from the viewpoint of near-ring theory (11), universal algebra (9), and at Vienna (10); recent advances include (8, 3). (3) Given a set S ofendomorphismsofa group G, compute the centralizer near-ring Ms(G). The centralizer near-ring is the near-ring of all mappings commuting with each single endomorphism in S; these near-rings playa central role in the structure theory of near-rings (5).