ABSTRACT
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 [4]) 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.
The purpose of this paper is to outline a general approach to the theory of Kro‐ necker function rings with coefficients in an integral domain D, by using semistai operations defined on D. This approach leads to relax the classical restrictions on D (not necessarily integrally closed) and on the (semi)star operations ⋆ (not necessarily endlich arithmetisch brauchbar) and it establishes a natural bridge with the “abstract” theory of Kronecker function rings recently developed by Halter‐Koch [7].
