Products of nilpotents in a quaternion ring of odd order

2025/12/23 by David Dolžan, Dolžan, David
Mathematics · Computer Science · #Finite Group Theory Research #Rings, Modules, and Algebras #Coding theory and cryptography

paper · doi:10.48550/arxiv.2512.20189

Abstract

Let R be a finite commutative local principal ring of cardinality qⁿ, where q = p^r for an odd prime p and integer r with R/J(R) ≃ GF(q). We determine the number of elements in the quaternion ring H(R) that can be expressed as a product of at least 2n-1 nilpotent elements, and show by example that this bound is sharp.

Citations

• Products of idempotents in a quaternion ring
• On the sumsets of exceptional units in quaternion rings
• Nil clean rings
• Lifting idempotents and exchange rings

Related

• Products of idempotents in a quaternion ring
• Unipotent orbits of elements in a quaternion ring of odd order
• On the sumsets of exceptional units in quaternion rings
• Generalized Quaternion Rings over ℤ/nℤ for an odd n
• A Note on Quaternions over Commutative Rings