ABSTRACT

A characterization of idempotency is given for triangular matrices with entries from an arbitrary ring. This yields an elementary approach to constructing such matrices. It also reveals structure allowing for the explicit enumeration or implicit counting of all idempotent triangular matrices over a given finite ring.

中文翻译：

---

一般环上的三角幂等矩阵

摘要

对于具有来自任意环的条目的三角形矩阵，给出了幂等性的表征。这产生了构造此类矩阵的基本方法。它还揭示了允许对给定有限环上的所有幂等三角矩阵进行显式枚举或隐式计数的结构。