On the primitivity of prime rings

DOI10.1016/0021-8693(79)90135-2zbMath0412.16002OpenAlexW2021469181MaRDI QIDQ1260148

Lance W. Small, Charles Lanski, Richard Resco

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0021-8693(79)90135-2

zbMATH Keywords

division algebraprime ringleft annihilatorprimitive ringnonzero idempotentprimitive F-algebra with nonzero socle

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Conditions on elements (16U99) Graded rings and modules (associative rings and algebras) (16W50) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Division rings and semisimple Artin rings (16Kxx)

Related Items (22)

Prime and primitive Kumjian–Pask algebras ⋮ Semigroup rings ⋮ On the tensor products of algebras ⋮ Semiprimeness of semigroup algebras ⋮ On normal classes of rings ⋮ Unions of chains of primes ⋮ On the ideals of ultragraph Leavitt path algebras ⋮ The Dixmier-Moeglin equivalence for Leavitt path algebras. ⋮ Growth, entropy and commutativity of algebras satisfying prescribed relations. ⋮ On prime nonprimitive von Neumann regular algebras ⋮ On graded primitive Leavitt path algebras ⋮ Associative rings ⋮ On primitive ideals in polynomial rings over nil rings. ⋮ Multiplicative Sets of Primitive Idempotents and Primitive Ideals ⋮ Primitivity of finitely presented monomial algebras. ⋮ Examples in finite Gel'fand-Kirillov dimension ⋮ The Dixmier-Moeglin equivalence, Morita equivalence, and homeomorphism of spectra ⋮ Normal classes of rings and tensor products ⋮ Graded irreducible representations of Leavitt path algebras: a new type and complete classification ⋮ Generalized Munn rings ⋮ A question of Kaplansky ⋮ Chains of prime ideals and primitivity of \(\mathbb Z\)-graded algebras.

Cites Work

• Polynomials over division rings
• Group rings of free products are primitive

This page was built for publication: On the primitivity of prime rings