Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 117-132 (2004)
Normalizing extensions of semiprime rings
Miguel Ferrero and Rogério Ricardo SteffenonInstituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900 Porto Alegre - RS, Brazil, e-mail: firstname.lastname@example.org; Centro de Ciências Exatas e Tecnológicas, Universidade do Vale do Rio dos Sinos, 93022-000 Sao Leopoldo - RS, Brazil, e-mail: email@example.com.
Abstract: In this paper we study normalizing extension of semiprime rings. For an extension $S$ of $R$ we construct the canonical torsion-free $S^*$, which is a normalizing extension of the symmetric ring of quotients $Q$ of $R$. We extend results which are known for centralizing extensions and for normalizing bimodules to one-to-one correspondence between closed ideals. Finally we study prime ideals, non-singular prime ideals and (right) strongly prime ideals of intermediate extensions.
Classification (MSC2000): 16D20, 16D30, 16S20, 16S90
Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.