On directly infinite rings

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

Authors

Mario Petrich (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: Acta Mathematica Hungarica

Vol. 85 No. 1-2

Pages: 153-165

ISSN: 0236-5294

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 3 Citations

ISI Web of Science

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-33M

DOI: 10.1023/a:1006633231817

Abstract (EN): A ring R with identity 1 is said to he directly finite if for any a, b is an element of R, ab = 1 implies that ba = 1; otherwise R is directly infinite. With AT the set of nonnegative integers, let B be the ring of N x N matrices over the ring of integers generated by two particular matrices. Properties of directly infinite rings are explored in relation to the ring B. This is made possible by various characterizations of the ring B one of which is that it is torsion free and generated by a bicyclic subsemigroup of its multiplicative semigroup. Some ideals and all idempotents of the ring B are constructed. The concepts of directly finite and chain finite idempotents are introduced in an arbitrary ring and applied to the ring B.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13