Classical Quotient Rings of Group Rings

Author

R. (Ralph) W. Wilkerson, Missouri University of Scieince and TechnologyFollow

Abstract

Throughout G Will Denote a Free Abelian Group and Z(R) the Right Singular Ideal of a Ring R. a Ring R is a Cl-Ring If R is (Goldie) Right Finite Dimensional, R/Z(R) is Semiprime, Z(R) is Rationally Closed, and Z(R) Contains No Closed Uniform Right Ideals. We Prove that R is a Cl-Ring If and Only If the Group Ring RG is a C1-Ring. If RG Has the Additional Property that BRG is Dense Whenever B is a Right Nonzero-Divisor, Then the Complete Ring of Quotients of RG is a Classical Ring of Quotients. © 1976 Taylor and Francis Group, LLC.

Recommended Citation

R. W. Wilkerson, "Classical Quotient Rings of Group Rings," Quaestiones Mathematicae, vol. 1, no. 2, pp. 219 - 224, National Inquiry Services Centre (NISC); Taylor and Francis; Taylor and Francis Group, Jan 1976.

The definitive version is available at https://doi.org/10.1080/16073606.1976.9632525

Department(s)

Computer Science

International Standard Serial Number (ISSN)

1727-933X; 1607-3606

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 National Inquiry Services Centre (NISC); Taylor and Francis; Taylor and Francis Group, All rights reserved.

Publication Date

01 Jan 1976