Local Rings of Rings of Quotients |
| |
Authors: | M. A. Gómez Lozano M. Siles Molina |
| |
Affiliation: | (1) Departamento de álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain |
| |
Abstract: | The aim of this paper is to characterize those elements in a semiprime ring R for which taking local rings at elements and rings of quotients are commuting operations. If Q denotes the maximal ring of left quotients of R, then this happens precisely for those elements if R which are von Neumann regular in Q. An intrinsic characterization of such elements is given. We derive as a consequence that the maximal left quotient ring of a prime ring with a nonzero PI-element is primitive and has nonzero socle. If we change Q to the Martindale symmetric ring of quotients, or to the maximal symmetric ring of quotients of R, we obtain similar results: an element a in R is von Neumann regular if and only if the ring of quotients of the local ring of R at a is isomorphic to the local ring of Q at a. Partially supported by the Ministerio de Educación y Ciencia and Fondos Feder, jointly, trough projects MTM2004-03845, MTM2007-61978 and MTM2004-06580-C02-02, MTM2007-60333, by the Junta de Andalucía, FQM-264, FQM336 and FQM02467 and by the Plan de Investigación del Principado de Asturias FICYT-IB05-017. |
| |
Keywords: | Semiprime ring Local ring at an element Ring of quotients PI-element |
本文献已被 SpringerLink 等数据库收录! |
|