Products of idempotents in a quaternion ring

2025/12/23 by David Dolžan, Dolžan, David · 1 citation
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra #Commutative Algebra and Its Applications

paper · doi:10.48550/arxiv.2512.20183

Abstract

Let R be a finite commutative local principal ring, and let H(R) denote the corresponding quaternion ring. We show that an element of H(R) is a product of idempotents if and only if it can be expressed as a product of two idempotents. Moreover, we obtain an explicit formula for the number of elements of H(R) admitting such a factorization.

Citations

• On the sumsets of exceptional units in quaternion rings
• On the structure of quaternion rings over ℤ/n ℤ
• Decomposition of Singular Matrices into Idempotents

Cited by

• Products of nilpotents in a quaternion ring of odd order

Related

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• On the sumsets of exceptional units in quaternion rings
• Decomposition of Singular Matrices into Idempotents
• A Note on Quaternions over Commutative Rings
• Unipotent orbits of elements in a quaternion ring of odd order