On directly infinite rings

• Tipo: Artigo em Revista Científica Internacional
• Data: 1999

Autores

Mario Petrich (Autor) Outra; Pedro V. Silva (Autor) FCUP

Revista

Título: Acta Mathematica Hungarica

Vol. 85 Nº 1-2

Páginas: 153-165

ISSN: 0236-5294

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 3 Citações

ISI Web of Science

Scopus - 3 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 13