Some properties on rings with units satisfying a group identity

Chia Hsin Liu

doi:10.1006/jabr.2000.8397

Some properties on rings with units satisfying a group identity

Chia Hsin Liu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

For convenience, a ring with units satisfying a group identity will be called a GI-ring. We show that GI-rings have the following properties which are also properites of PI-rings. (1) Any GI-ring is Dedekind finite (von Neumann finite). (2) Nilpotent elements of a semiprimitive GI-ring have bounded index. (3) The Kurosh problem has a positive answer for GI-algebras, namely, any algebraic GI-algebra is locally finite. We also study Hartley's problem for algebraic GI-algebras.

Original language	English
Pages (from-to)	226-235
Number of pages	10
Journal	Journal of Algebra
Volume	232
Issue number	1
DOIs	https://doi.org/10.1006/jabr.2000.8397
Publication status	Published - 2000 Oct 1
Externally published	Yes

Keywords

Algebraic algebras
Dedekind finite
Group identities
Kurosh problem
Matrix units
Polynomial identities
Semiprimitive rings
semiprime rings

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jabr.2000.8397

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AB - For convenience, a ring with units satisfying a group identity will be called a GI-ring. We show that GI-rings have the following properties which are also properites of PI-rings. (1) Any GI-ring is Dedekind finite (von Neumann finite). (2) Nilpotent elements of a semiprimitive GI-ring have bounded index. (3) The Kurosh problem has a positive answer for GI-algebras, namely, any algebraic GI-algebra is locally finite. We also study Hartley's problem for algebraic GI-algebras.

KW - Algebraic algebras

KW - Dedekind finite

KW - Group identities

KW - Kurosh problem

KW - Matrix units

KW - Polynomial identities

KW - Semiprimitive rings

KW - semiprime rings

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JO - Journal of Algebra

JF - Journal of Algebra

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ER -

Some properties on rings with units satisfying a group identity

Abstract

Keywords

ASJC Scopus subject areas

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