Some properties on rings with units satisfying a group identity

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11 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 languageEnglish
Pages (from-to)226-235
Number of pages10
JournalJournal of Algebra
Volume232
Issue number1
DOIs
Publication statusPublished - 2000 Oct 1

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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