On semilocal modules and rings

• Type: Article in International Scientific Journal
• Date: 1999

Authors

lomp, christian (Author) FCUP

Journal

Title: Communications in Algebra

Vol. 27 No. 4

Pages: 1921-1935

ISSN: 0092-7872

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 56 Citations

Scopus - 49 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-007-8W5

DOI: 10.1080/00927879908826539

Resumo (PT): It is well-known that a ring R is semiperfect if and only if RR (or R R) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or R R) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie dimension) of modules is of interest and yields a natural interpretation of the Camps-Dicks characterization of semilocal rings. Finitely generated modules are weakly supplemented if and only if they have finite hollow dimension (or are semilocal).

Abstract (EN): It is well-known that a ring R is semiperfect if and only if R-R (or R-R) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if R-R (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie dimension) of modules is of interest and yields a natural interpretation of the Camps-Dicks characterization of semilocal rings. Finitely generated modules are weakly supplemented if and only if they have finite hollow dimension (or are semilocal).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15