Nonmatrix varieties and nil-generated algebras whose units satisfy a group identity

DOI10.1006/jabr.1996.6892zbMath0876.16020OpenAlexW1981232701MaRDI QIDQ1355571

Vladimir Tasić, David M. Riley, Yuly Billig

Publication date: 26 June 1997

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

Full work available at URL: https://doi.org/10.1006/jabr.1996.6892

zbMATH Keywords

groups of unitspolynomial identitiesgroup identitiesnil-generated algebrasnonmatrix identities

Mathematics Subject Classification ID

Group rings (16S34) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Units, groups of units (associative rings and algebras) (16U60)

Related Items (24)

Group algebras whose p-elements form a subgroup ⋮ Some identities on twisted group algebras ⋮ Group algebras and enveloping algebras with nonmatrix and semigroup identities ⋮ THE TRANSFER OF A COMMUTATOR IDENTITY IN A NIL-GENERATED ALGEBRA ⋮ ON NIL SUBSEMIGROUPS OF RINGS WITH GROUP IDENTITIES ⋮ Unnamed Item ⋮ A 5-Engel associative algebra whose group of units is not 5-Engel ⋮ GROUP IDENTITIES IN INCIDENCE RINGS ⋮ Nil-generated algebras and group algebras whose units satisfy a Laurent polynomial identity ⋮ When is a power of the Frobenius map on a noncommutative ring a homomorphism? ⋮ Multiplicatively collapsing and rewritable algebras ⋮ Non-matrix polynomial identity enveloping algebras ⋮ Star-group identities and groups of units. ⋮ On Laurent polynomial identities ⋮ Lie solvable enveloping algebras of characteristic two ⋮ Group identities on the units of algebraic algebras with applications to restricted enveloping algebras. ⋮ Group identities on units of group algebras ⋮ Characterization of non-matrix varieties of associative algebras. ⋮ On group identities for the unit group of algebras and semigroup algebras over an infinite field. ⋮ Some properties on rings with units satisfying a group identity ⋮ Group algebras with units satisfying an Engel identity ⋮ On units of twisted group algebras ⋮ Identities on units of algebraic algebras ⋮ Group identities on units of locally finite algebras and twisted group algebras

Cites Work

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• Nonmatrix varieties
• The Lie structure of enveloping algebras
• Group identities on units of rings
• The tensor product of Lie soluble algebras
• Existence of identities in \(A \otimes B\)
• Lie algebra associated with linear group
• Group algebras whose units satisfy a group identity
• Group algebras whose units satisfy a group identity. II
• Polynomial Identities in Graded Group Rings, Restricted Lie Algebras and p-Adic Analytic Groups
• Rings with a polynomial identity

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