On prime ideals and radicals of polynomial rings and graded rings.

DOI10.1016/j.jpaa.2013.06.004zbMath1287.16038OpenAlexW1986108344MaRDI QIDQ392422

Pjek-Hwee Lee, Edmund R. Puczylowski

Publication date: 14 January 2014

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2013.06.004

zbMATH Keywords

nilpotent elementsJacobson radicalKöthe problemprime ringspolynomial ringsBrown-McCoy radicalgraded ringsnil radicalLaurent polynomial rings

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Prime and semiprime associative rings (16N60) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Graded rings and modules (associative rings and algebras) (16W50) Ideals in associative algebras (16D25) General radicals and associative rings (16N80)

Related Items

On graded special radicals of graded rings, On the Jacobson radical of a groupoid graded ring, On arbitrarily graded rings, Notes on the graded Jacobson radical: a graded version of the Jacobson stable set, The upper nilradical and Jacobson radical of semigroup graded rings., On graded Thierrin radicals of graded rings, On radicals of graded ring constructions, On the Jacobson and simple radicals of semigroups, Chains of prime ideals and primitivity of \(\mathbb Z\)-graded algebras.

Cites Work

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• A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS
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• The jacobson and brown-mccoy radicals of rings graded by free groups
• Polynomial rings over nil rings cannot be homomorphically mapped onto rings with nonzero idempotents
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