Nagata Rings, Kronecker Function Rings and Related Semistar Operations

Simple item page
dc.creatorFontana, Marco
dc.creatorLoper, K. Alan
dc.date2003-02-13
dc.date.accessioned2026-07-07T04:55:17Z
dc.date.available2026-07-07T04:55:17Z
dc.descriptionIn 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book \cite{G}) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Prüfer and P. Lorenzen from 1930's. In \cite{FL1} and \cite{FL2} the current authors investigated properties of the Kronecker function rings which arise from arbitrary semistar operations on an integral domain $D$. In this paper we extend that study and also generalize Kang's notion of a star Nagata ring \cite{Kang:1987} and \cite{Kang:1989} to the semistar setting. Our principal focuses are the similarities between the ideal structure of the Nagata and Kronecker semistar rings and between the natural semistar operations that these two types of function rings give rise to on $D$.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0302163
dc.identifierhttp://arxiv.org/abs/math/0302163
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66524
dc.subjectCommutative Algebra
dc.subject13F05; 13A15; 13G05
dc.titleNagata Rings, Kronecker Function Rings and Related Semistar Operations
dc.typetext

Files

Collections

arXiv