Examples of Armendariz Rings

DOI10.1080/00927870903337968zbMath1218.16013OpenAlexW2008764240MaRDI QIDQ5390554

Ramon Antoine

Publication date: 4 April 2011

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

Full work available at URL: https://doi.org/10.1080/00927870903337968

zbMATH Keywords

nilpotent elementspolynomial ringsBaer ringssemicommutative ringsArmendariz ringsreversible ringsnil-Armendariz ringspp-ringszip rings

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) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items (15)

Nilpotent polynomials and nilpotent coefficients ⋮ Amalgamated rings with clean-type properties ⋮ \(\mathcal{Z}\)-Armendariz rings and modules ⋮ Further results on central Armendariz rings ⋮ Nil-Armendariz condition on skew generalized power series rings ⋮ On power series Armendariz modules ⋮ On partial-Armendariz rings ⋮ On linearly weak Armendariz rings. ⋮ Power serieswise Armendariz property in amalgamated algebra ⋮ Polynomial Rings Over Weak Armendariz Rings need not be Weak Armendariz ⋮ A GENERALIZATION OF NIL-ARMENDARIZ RINGS ⋮ Unnamed Item ⋮ Armendariz group rings ⋮ On Z-symmetric rings ⋮ Distributive modules and Armendariz modules.

Cites Work

• Nilpotent elements and Armendariz rings.
• Two counterexamples in power series rings
• Armendariz rings
• Extensions of reversible rings.
• Polynomial rings over nil rings need not be nil
• Extensions of zip rings.
• Armendariz rings and reduced rings
• The polynomial ring over a Goldie ring need not be a Goldie ring
• Armendariz and Reduced Rings
• Zip rings and mal'cev domains
• Armendariz rings and gaussian rings
• A note on extensions of Baer and P. P. -rings
• ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS
• New good quasi-cyclic codes over GF(3)
• Power Series Rings Satisfying a Zero Divisor Property
• On Weak Armendariz Rings
• Polynomials rings over Goldie rings
• On annihilator ideals of a polynomial ring over a noncommutative ring

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