Armendariz and Reduced Rings

DOI10.1081/AGB-120037221zbMath1068.16037OpenAlexW2017729663WikidataQ57788241 ScholiaQ57788241MaRDI QIDQ3158211

Tsiu-Kwen Lee, Yiqiang Zhou

Publication date: 21 January 2005

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/agb-120037221

zbMATH Keywords

matrix ringstrivial extensionsArmendariz ringsreduced rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Ordinary and skew polynomial rings and semigroup rings (16S36) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Centralizing and normalizing extensions (16S20)

Related Items (51)

ON STRONG SYMMETRIC RINGS AND THEIR EXTENSIONS ⋮ On Rings Having McCoy-Like Conditions ⋮ Reflexive Property of Rings ⋮ Power-serieswise McCoy Rings ⋮ Zero Divisors in Skew Power Series Rings ⋮ Extensions of Generalized Armendariz Rings ⋮ On a class of semicommutative modules. ⋮ A GENERALIZATION OF REDUCED RINGS ⋮ ANNIHILATOR CONDITIONS IN MATRIX AND SKEW POLYNOMIAL RINGS ⋮ ON WEAKLY RIGID RINGS ⋮ On strongly \(J_n\)-clean rings ⋮ McCoy property and nilpotent elements of skew generalized power series rings ⋮ Special properties of the ring Sn(R) ⋮ Generalized quasi-Baer *-rings and Banach *-algebras ⋮ Nilpotent elements and nil-Armendariz property of skew generalized power series rings ⋮ A note on weakly nil-clean rings ⋮ On Armendariz Rings and Matrix Rings with Simple 0-Multiplication ⋮ Rings whose singular ideals are nil ⋮ The McCoy condition on skew monoid rings ⋮ The Armendariz property on ideals. ⋮ Unnamed Item ⋮ Pseudo-Differential Operator Rings with Armendariz-Like Condition ⋮ Examples of Armendariz Rings ⋮ The Armendariz module and its application to the Ikeda-Nakayama module. ⋮ Rings with property (A) and their extensions. ⋮ The rings where zero-divisor polynomials have zero-divisor coefficients ⋮ On Skew Armendariz of Laurent Series Type Rings ⋮ On skew polynomials over Ikeda-Nakayama rings ⋮ Radicals of Skew Polynomial and Skew Laurent Polynomial Rings Over Skew Armendariz Rings ⋮ Involutive triangular matrix algebras ⋮ Annihilator conditions on polynomials over modules. ⋮ Unnamed Item ⋮ Maximal Semicommutative Subrings of Upper Triangular Matrix Rings ⋮ On Radicals of Skew Inverse Laurent Series Rings ⋮ The minimal prime spectrum of rings with annihilator conditions. ⋮ Noetherian properties in composite generalized power series rings ⋮ Armendariz group rings ⋮ RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT ⋮ Weak Quasi-Armendariz Rings ⋮ On α-nilpotent elements and α-Armendariz rings ⋮ On Skew Power Serieswise Armendariz Rings ⋮ The McCoy Condition on Skew Polynomial Rings ⋮ Varieties of rings, where all subdirectly irreducible finite rings are Armendariz ones. ⋮ Armendariz and SFT properties in subring retracts ⋮ Special Properties of Rings of Skew Generalized Power Series ⋮ Unnamed Item ⋮ On Constant Zero-Divisors of Linear Polynomials ⋮ Ideal-Symmetric and Semiprime Rings ⋮ ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS ⋮ A REMARK ON IFP RINGS ⋮ Distributive modules and Armendariz modules.

Cites Work

• Armendariz rings
• Ore extensions of Baer and p.p.-rings.
• Armendariz rings and reduced rings
• The polynomial ring over a Goldie ring need not be a Goldie ring
• Armendariz rings and gaussian rings
• A note on extensions of Baer and P. P. -rings
• ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS
• On annihilator ideals of a polynomial ring over a noncommutative ring

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