Prime ideals in PI-rings

DOI10.1016/0021-8693(80)90188-XzbMath0424.16009WikidataQ105486873 ScholiaQ105486873MaRDI QIDQ1134794

S. A. Amitsur, Lance W. Small

Publication date: 1980

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

zbMATH Keywords

ring of quotientsgeneric matricescenter of ringsaffine prime PI-ringsfinitely generated prime PI-algebraprime ideals in PI-ringsright noetherian PI G-ring

Mathematics Subject Classification ID

Rings with polynomial identity (16Rxx) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (22)

A Springer theorem for Hermitian forms. ⋮ Trace rings of generic matrices are unique factorization domains ⋮ The principal ideal theorem in prime Noetherian rings ⋮ First-order rigidity of rings satisfying polynomial identities ⋮ Localization in Noetherian P.I. rings as a finite criterion ⋮ Symmetry and localization in Noetherian prime PI rings ⋮ Polynomial identity rings as rings of functions. ⋮ Semi-hereditary orders in a simple artinian ring ⋮ Jacobson rings with a polynomial identity ⋮ Polynomial identity rings as rings of functions. II. ⋮ Some remarks on growth of algebras over commutative noetherian rings ⋮ Krull and Global Dimensions of Semiprime Noetherian PI-Rings ⋮ On the intersection property of Dubrovin valuation rings ⋮ On Dubrovin Valuation Rings in Crossed Product Algebras ⋮ Modules over regular algebras of dimension 3 ⋮ Maximal orders over valuation rings ⋮ Associative rings ⋮ Value functions and associated graded rings for semisimple algebras ⋮ Localization at height one prime ideals in affine prime PI rings ⋮ Finite Extensions of Rings ⋮ The nilpotency of the radical in a finitely generated P.I. ring ⋮ An additivity principle for p.i. rings

Cites Work

• Right Noetherian rings integral over their centers
• Principal ideal theorem for Noetherian P.I.rings
• The Jacobson radical in PI-algebras
• Non-commutative affine P. I. rings are catenary
• Liberal Extensions
• Relative krull dimension and prime ideals in right noetherian rings
• Prime 𝑃𝐼-rings
• ON THE DIMENSION OF NONCOMMUTATIVE AFFINE ALGEBRAS
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