Armendariz rings
From MaRDI portal
Publication:1357060
DOI10.3792/pjaa.73.14zbMath0960.16038OpenAlexW4251336894MaRDI QIDQ1357060
Publication date: 20 July 1997
Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3792/pjaa.73.14
Endomorphism rings; matrix rings (16S50) Ordinary and skew polynomial rings and semigroup rings (16S36) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)
Related Items
REVERSIBILITY OVER UPPER NILRADICALS ⋮ Reflexive ideals and reflexively closed subsets in rings ⋮ On rings with weak property (A) and their extensions ⋮ ON STRONG SYMMETRIC RINGS AND THEIR EXTENSIONS ⋮ Extensions of Generalized Armendariz Rings ⋮ On Skew Armendariz Rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ ON GENERALIZED ZIP RINGS ⋮ ON WEAK ARMENDARIZ MODULES ⋮ A REMARK ON LEFT NEAR-COMMUTATIVITY ⋮ Extensions of McCoy Rings ⋮ ON Π-NEAR-ARMENDARIZ RINGS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Domain property of rings relative to the Jacobson radical ⋮ Skew McCoy rings and σ-compatibility ⋮ On \(\mathcal{Z}\)-reversible rings ⋮ Nilpotent elements and nil-Armendariz property of skew generalized power series rings ⋮ On a theorem of McCoy ⋮ Symmetricity of rings relative to the prime radical ⋮ On nilpotent elements of ore extensions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On partial-Armendariz rings ⋮ Symmetric property of rings with respect to the Jacobson radical ⋮ GRADED UNIFORMLY pr-IDEALS ⋮ Unified Extensions of Strongly Reversible Rings and Links with Other Classic Ring Theoretic Properties ⋮ Pseudo-Differential Operator Rings with Armendariz-Like Condition ⋮ Examples of Armendariz Rings ⋮ On Armendariz-like properties in amalgamated algebras along ideals ⋮ Strongly CM -semicommutative rings ⋮ Nil-Armendariz rings relative to a monoid. ⋮ McCOY PROPERTY OF SKEW LAURENT POLYNOMIALS AND POWER SERIES RINGS ⋮ Rings whose nilpotents form a multiplicative set ⋮ RADICALS OF SKEW GENERALIZED POWER SERIES RINGS ⋮ McCoy rings of path algebras and truncated algebras ⋮ On Skew Armendariz of Laurent Series Type Rings ⋮ On skew polynomials over Ikeda-Nakayama rings ⋮ NIL-ARMENDARIZ RINGS AND UPPER NILRADICALS ⋮ On Monoid Rings Over Nil Armendariz Ring ⋮ The McCoy Condition on Ore Extensions ⋮ Radicals of Skew Polynomial and Skew Laurent Polynomial Rings Over Skew Armendariz Rings ⋮ Polynomial Rings Over Weak Armendariz Rings need not be Weak Armendariz ⋮ Reversibility of skew Hurwitz series rings ⋮ Skew Hurwitz serieswise quasi-Armendariz rings ⋮ On Nagata rings with amalgamation properties ⋮ MAL'CEV–NEUMANN SERIES OVER ZIP AND WEAK ZIP RINGS ⋮ TRIANGULAR MATRIX REPRESENTATION OF SKEW GENERALIZED POWER SERIES RINGS ⋮ Nil-Armendariz rings relative to a monoid. ⋮ REGULARITY AND STRONG REGULARITY IN THE CONTEXT OF CERTAIN CLASSES OF RINGS ⋮ A GENERALIZATION OF NIL-ARMENDARIZ RINGS ⋮ Armendariz modules over skew PBW extensions ⋮ Unnamed Item ⋮ Extensions of Generalized Reduced Rings ⋮ ARMENDARIZ RINGS RELATIVE TO A MONOID ⋮ Unnamed Item ⋮ On nil-McCoy rings relative to a monoid ⋮ A note on lower nil M-Armendariz rings ⋮ Unnamed Item ⋮ On annihilator ideals of a polynomial ring over a noncommutative ring ⋮ Ore Extensions of Skew Armendariz Rings ⋮ Skew polynomial rings over σ-skew Armendariz rings ⋮ Generalized Quasi-Baer Rings ⋮ ABELIAN PROPERTY CONCERNING FACTORIZATION MODULO RADICALS ⋮ ON A RING PROPERTY GENERALIZING POWER-ARMENDARIZ AND CENTRAL ARMENDARIZ RINGS ⋮ REVERSIBILITY OVER PRIME RADICALS ⋮ INSERTION-OF-FACTORS-PROPERTY WITH FACTORS NILPOTENTS ⋮ Armendariz group rings ⋮ Power Series Rings Satisfying a Zero Divisor Property ⋮ On α-nilpotent elements and α-Armendariz rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Eversible and reversible semigroups and semirings ⋮ On Weak Armendariz Rings ⋮ Unnamed Item ⋮ Special Properties of Rings of Skew Generalized Power Series ⋮ Unnamed Item ⋮ Reflexive property on rings with involution ⋮ When is a Sum of Annihilator Ideals an Annihilator Ideal? ⋮ On some classes of reflexive rings ⋮ McCoy property of Hurwitz series rings ⋮ On Constant Zero-Divisors of Linear Polynomials ⋮ On Generalizations of Commutativity ⋮ Unnamed Item ⋮ Rings which satisfy the Property of Inserting Regular Elements at Zero Products ⋮ A PROOF ON POWER-ARMENDARIZ RINGS ⋮ ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS ⋮ A REMARK ON IFP RINGS ⋮ ON COEFFICIENTS OF NILPOTENT POLYNOMIALS IN SKEW POLYNOMIAL RINGS ⋮ RINGS OVER WHICH POLYNOMIAL RINGS ARE ARMENDARIZ AND REVERSIBLE ⋮ On a ring property related to nilradicals ⋮ Quasi-central Armendariz rings ⋮ On annihilator ideals in skew power series rings ⋮ Nilradicals of the unique product monoid rings ⋮ ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS ⋮ McCoy modules and related modules over commutative rings ⋮ Left Nil Zero Semicommutative rings ⋮ \(\Sigma\)-semicommutative rings and their skew PBW extensions ⋮ On Skew Inverse Laurent-Serieswise Armendariz Rings ⋮ A note on essential Ikeda-Nakayama rings ⋮ Armendariz and Reduced Rings ⋮ Special Properties of Rings of Generalized Power Series ⋮ On Rings Having McCoy-Like Conditions ⋮ Reflexive Property of Rings ⋮ ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS ⋮ Nilpotent polynomials and nilpotent coefficients ⋮ Zero Divisors in Skew Power Series Rings ⋮ On a class of semicommutative modules. ⋮ On zip and weak zip rings of skew generalized power series. ⋮ Strongly semicommutative rings relative to a monoid. ⋮ Idealization of a module ⋮ A GENERALIZATION OF REDUCED RINGS ⋮ ANNIHILATOR CONDITIONS IN MATRIX AND SKEW POLYNOMIAL RINGS ⋮ NILPOTENT ELEMENTS AND NIL-ARMENDARIZ PROPERTY OF MONOID RINGS ⋮ ORE EXTENSIONS OF WEAK ZIP RINGS ⋮ ON RINGS WHOSE RIGHT ANNIHILATORS ARE BOUNDED ⋮ EXTENSIONS OF α-REFLEXIVE RINGS ⋮ On some results and open problems concerning Armendariz rings ⋮ \(\pi\)-Armendariz rings relative to a monoid ⋮ ON NIL SKEW ARMENDARIZ RINGS ⋮ An alternative perspective on skew generalized power series rings ⋮ On skew Hurwitz serieswise Armendariz rings ⋮ \(\mathcal{Z}\)-Armendariz rings and modules ⋮ Structure of insertion property by powers ⋮ Ring properties related to symmetric rings ⋮ Semirings of skew Laurent polynomials ⋮ Weak \(\alpha\)-skew Armendariz ideals. ⋮ McCoy property and nilpotent elements of skew generalized power series rings ⋮ Semi-Baer modules ⋮ Further results on central Armendariz rings ⋮ \(\sigma \)-PBW extensions of skew Armendariz rings ⋮ Special properties of the ring Sn(R) ⋮ Quasi-Armendariz Rings Relative to a Monoid ⋮ On Armendariz Rings and Matrix Rings with Simple 0-Multiplication ⋮ Nil-Armendariz condition on skew generalized power series rings ⋮ Symmetric ring property on nil ideals ⋮ Zero-Divisor Graphs of Laurent Polynomials and Laurent Power Series ⋮ On power series Armendariz modules ⋮ Reflexive property on nil ideals ⋮ Extensions of reversible rings. ⋮ The Armendariz property on ideals. ⋮ Reflexive property restricted to nilpotents ⋮ On classical quotient rings of skew Armendariz rings. ⋮ Zero-divisor placement, a condition of Camillo, and the McCoy property ⋮ Armendariz rings and reduced rings ⋮ Generalized Rigid Modules and Their Polynomial Extensions ⋮ Nilpotent elements and Armendariz rings. ⋮ On linearly weak Armendariz rings. ⋮ Rings in which nilpotent elements are right singular ⋮ Power serieswise Armendariz property in amalgamated algebra ⋮ Rings with property (A) and their extensions. ⋮ Extended Semicommutative Rings ⋮ Skew Poincaré-Birkhoff-Witt extensions over weak zip rings ⋮ McCoy Rings Relative to a Monoid ⋮ A UNIFIED APPROACH TO VARIOUS GENERALIZATIONS OF ARMENDARIZ RINGS ⋮ Insertion-of-factors-property skewed by ring endomorphisms ⋮ Unnamed Item ⋮ Armendariz rings and gaussian rings ⋮ Extensions of zip rings. ⋮ Right Gaussian rings and skew power series rings. ⋮ A note on nil power serieswise Armendariz rings. ⋮ Duo, Bézout, and distributive rings of skew power series. ⋮ Unnamed Item ⋮ Some remarks on one-sided regularity ⋮ On Extended Reversible Rings ⋮ Quasi-Armendariz rings relative to a monoid. ⋮ Quasi-Armendariz generalized power series rings ⋮ Annihilator Ideals of Noncommutative Ring Constructions ⋮ Extension of Antoine's ring construction ⋮ On constant Armendariz rings ⋮ GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE ⋮ Unnamed Item ⋮ Radicals of Ore Extension of Skew Armendariz Rings ⋮ Baer and Quasi-Baer Properties of Skew Generalized Power Series Rings ⋮ Radicals and Köthe's conjecture for skew PBW extensions ⋮ A new class of unique product monoids with applications to ring theory. ⋮ ARMENDARIZ AND QUASI-ARMENDARIZ SEMIRINGS AND PS SEMIRINGS ⋮ Reflexive-nilpotents-property skewed by ring endomorphisms ⋮ Ring endomorphisms satisfying the central reversible property ⋮ Generalizations of reversible and Armendariz rings ⋮ RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT ⋮ Weak Quasi-Armendariz Rings ⋮ On Z-symmetric 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 ⋮ Radicals of Skew Inverse Laurent Series Rings ⋮ Armendariz-like properties in bi-amalgamations ⋮ Armendariz Properties Relative to a Ring Endomorphism ⋮ Basic examples and extensions of symmetric rings. ⋮ Insertion of units at zero products ⋮ Ideal-Symmetric and Semiprime Rings ⋮ Reversible ring property via idempotent elements ⋮ Abelian right McCoy rings and related notions ⋮ On modules related to McCoy modules ⋮ Distributive modules and Armendariz modules. ⋮ On Sums of Coefficients of Products of Polynomials
Cites Work
