Idempotents in triangular matrix rings

2019/03/22 by Xin Hou · 1 citation
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Algebraic structures and combinatorial models

paper · doi:10.1080/03081087.2019.1596223

Abstract

Let R be an associative ring with identity 1. We describe all idempotent matrices with only zeros and ones on the diagonal in T(n,R) – the ring of n×n upper triangular matrices over R (n∈N), and T(∞,R) – the ring of infinite upper triangular matrices (indexed by N) over R. Moreover, when R is finite, we calculate the number of all idempotent matrices with only zeros and ones on the diagonal in T(n,R).

Citations

• Decomposition of singular matrices into idempotents
• When is a matrix a difference of two idempotents

Cited by

• Strongly nil-clean 2-by-2 matrices over general commutative rings

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