上三角矩阵环的两类半交换Armendariz子环

Two Classes of Semicommutative Armendariz Subrings of Upper Triangular Matrix Rings

摘要

利用约化环理论研究上三角矩阵环的半交换和Armendariz性质,基于具有相容自同态的环,构造给出了四阶上三角矩阵环的两类半交换Armendariz子环.

Abstract

By using the theory of reduced rings, we studied the semicommutative and Armendariz properties of upper triangular matrix rings. Based on rings with compatible endomorphisms, we constructed and gave two classes of semicommutative Armendariz subrings of the fourth-order upper triangular matrix ring.

关键词

约化环 / Euclid整环 / 相容自同态 / 半交换环 / Armendariz环

Key words

reduced ring / Euclidean domain / compatible endomorphism / semicommutative ring / Armendariz ring

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基金资助

国家自然科学基金(12161069)

兰州交通大学“科研反哺教学典型案例”教学改革研究项目(JGY202508)