Rings and finite fields whose elements are sums or differences of tripotents and potents

DOI10.55730/1300-0098.3543MaRDI QIDQ6618867

D. T. Tapkin, Peter Danchev, A. N. Abyzov, Stephen D. Cohen

Publication date: 15 October 2024

Published in: Turkish Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

unitsidempotentsfinite fieldsGauss and Jacobi sumstripotentspotents(weakly) \(n\)-torsion clean rings

Mathematics Subject Classification ID

Group rings (16S34) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Units, groups of units (associative rings and algebras) (16U60)

Cites Work

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• On runs of consecutive quadratic residues and quadratic nonresidues
• When is every matrix over a ring the sum of two tripotents?
• Rings over which matrices are sums of idempotent and \(q \)-potent matrices
• Weakly clean rings and almost clean rings
• Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum.
• Consecutive Primitive Roots in a Finite Field
• 𝑛-torsion clean rings
• On consecutive primitive elements in a finite field
• On rings with xn − x nilpotent

Related Items (1)

Representability of matrices over commutative rings as sums of two potent matrices

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