Similarity for zero-square matrices

2021/08/29 by Grigore Călugăreanu, Calugareanu, Grigore
Engineering · Mathematics · #15B33 #16U100 #16U30 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2108.12882

openalex publication_date 2021/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let T be an n by n zero-square matrix over a commutative unital ring R. We show that T is similar to a multiple of E₁n if R is a GCD domain and n = 2, if R is a GCD domain with 2 not zero divisor and n = 3, but there are matrices which are not similar to any multiple of E₁n whenever n greater or equal 4, over any commutative unital ring.

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