Primitive Near-rings-Some Structure Theorems

• 来源期刊: 代数集刊(英文版)
• 关键词: sandwich near-rings primitive near-rings regular semigroups
• 年，卷（期）: 2007,（3）
• 页码范围: 417-424
• 页数: 8页
• 语种: 英文

摘要

We show that any zero symmetric 1-primitive near-ring with descending chain condition on left ideals can be described as a centralizer near-ring in which the multipli-cation is not the function composition but sandwich multiplication.This result follows from a more general structure theorem on 1-primitive near-rings with multiplicative right identity,not necessarily having a chain condition on left ideals.We then use our results to investigate more closely the multiplicative semigroup of a 1-primitive near-ring.In par-ticular,we show that the set of regular elements forms a right ideal of the multiplicative semigroup of the near-ring.