Abstract

After recalling the motivations that led to the classical constructions of the Kronecker funtion ring and the Nagata ring, in this talk I will present some recent developments related to these constructions, in connection with a new approach to the theory of multiplicative ideal systems in integral domains. In particular, given a Krull's star operation (or a semistar operation, in the sense of Okabe-Matsuda) $\star$ on an integral domain $D$, I will discuss the relations between the multiplicative structure of the ideals in the general constructions of the Nagata ring Na$(D, \star)$ and Kronecker function ring Kr$(D, \star)$ and I will present some results obtained recently in a joint work with Alan Loper (Ohio State University).



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