Some properties on rings with units satisfying a group identity

JOURNAL OF ALGEBRA

卷:232

Article

Liu, CH

关键词: group identities;    polynomial identities;    matrix units;    Dedekind finite;    semiprime rings;    semiprimitive rings;    Kurosh problem;    algebraic algebras;   

DOI  :  10.1006/jabr.2000.8397

来源: Elsevier

【 摘 要 】

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. (C) 2000 Academic Press.

【 授权许可】

Free