2003/02/13 by Marco Fontana, Fontana, Marco, K. Alan Loper +1
Mathematics · #13A15 #13F05 #13G05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A15 #msc:13F05 #msc:13G05
paper · pdf · doi:10.48550/arxiv.math/0302163
20 pages
arxiv created 2003/02/13 · arxiv updated 2009/11/30
In 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 \citeG) 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 \citeFL1 and \citeFL2 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 \citeKang:1987 and \citeKang: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.