RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT

DOI10.1142/S0218196711006431zbMath1233.16031OpenAlexW2035538844MaRDI QIDQ3094336

Yang Lee, Tai Keun Kwak

Publication date: 24 October 2011

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196711006431

zbMATH Keywords

polynomial ringsvon Neumann regular ringsnil-Armendariz ringsCN-ringsnilpotent polynomials

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Generalizations of commutativity (associative rings and algebras) (16U80) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (17)

Nilpotent polynomials and nilpotent coefficients ⋮ An alternative perspective on skew generalized power series rings ⋮ Skew McCoy rings and σ-compatibility ⋮ The Armendariz property on ideals. ⋮ Reflexive property restricted to nilpotents ⋮ Zero-divisor placement, a condition of Camillo, and the McCoy property ⋮ McCOY PROPERTY OF SKEW LAURENT POLYNOMIALS AND POWER SERIES RINGS ⋮ The rings where zero-divisor polynomials have zero-divisor coefficients ⋮ ON A RING PROPERTY GENERALIZING POWER-ARMENDARIZ AND CENTRAL ARMENDARIZ RINGS ⋮ Reflexive-nilpotents-property skewed by ring endomorphisms ⋮ Generalizations of reversible and Armendariz rings ⋮ Unnamed Item ⋮ Reflexive property on rings with involution ⋮ McCoy property of Hurwitz series rings ⋮ On Constant Zero-Divisors of Linear Polynomials ⋮ ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS ⋮ On Sums of Coefficients of Products of Polynomials

Cites Work

• Unnamed Item
• Structure and topological conditions of NI rings.
• Nilpotent elements and Armendariz rings.
• Armendariz rings
• Nil ideals in rings with finite Krull dimension
• Polynomial rings over nil rings need not be nil
• Armendariz rings and reduced rings
• McCoy rings and zero-divisors.
• Semi-commutativity and the McCoy condition.
• ON 2-PRIMAL ORE EXTENSIONS
• Armendariz and Reduced Rings
• Radicals Of Polynomial Rings
• A note on extensions of Baer and P. P. -rings
• ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS
• An Ascending Chain Condition on Wedderburn Radicals
• Nil Subrings of Goldie Rings are Nilpotent
• A question on McCoy rings

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