Some properties on rings with units satisfying a group identity

DOI10.1006/jabr.2000.8397zbMath0967.16012OpenAlexW2081233839MaRDI QIDQ1588400

Chia-Hsin Liu

Publication date: 16 July 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8397

zbMATH Keywords

groups of unitsnilpotent idealssemiprime algebrasgroup identitiesPI-ringsGI-rings

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Units, groups of units (associative rings and algebras) (16U60)

Related Items (16)

Some identities on twisted group algebras ⋮ ON NIL SUBSEMIGROUPS OF RINGS WITH GROUP IDENTITIES ⋮ GROUP IDENTITIES IN INCIDENCE RINGS ⋮ On the unit groups of rings with involution ⋮ Permutable subgroups in \(\mathrm{GL}_n (D)\) and applications to locally finite group algebras ⋮ On Laurent polynomial identities ⋮ Locally solvable unit group of crossed products ⋮ Group identities on the units of algebraic algebras with applications to restricted enveloping algebras. ⋮ On group identities for the unit group of algebras and semigroup algebras over an infinite field. ⋮ Identities on Maximal Subgroups of GL_n(D) ⋮ Invertibility and Dedekind finiteness in structural matrix rings ⋮ Algebras whose units satisfy a \(*\)-Laurent polynomial identity ⋮ Some algebraic algebras with Engel unit groups ⋮ Additive mappings and identities on unit groups of algebraic algebras ⋮ On units of twisted group algebras ⋮ Identities on units of algebraic algebras

Cites Work

• Symmetric units and group identities
• Group identities on units of rings
• Nonmatrix varieties and nil-generated algebras whose units satisfy a group identity
• Rational identities and applications to algebra and geometry
• Group algebras with units satisfying a group identity
• Group algebras with units satisfying a group identity II
• On free subgroups of units of rings
• Group algebras whose units satisfy a group identity
• Group algebras whose units satisfy a group identity. II
• Group identities on units of locally finite algebras and twisted group algebras
• Conjugates in Prime Rings
• Unnamed Item
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