Korean J. Math.  Vol 20, No 4 (2012)  pp.
DOI: https://doi.org/10.11568/kjm.2012.20.4.

KRONECKER FUNCTION RINGS AND PRUFER-LIKE DOMAINS

Gyu Whan Chang

Abstract


Let $D$ be an integral domain, $D$ be the integral closure of $D$, $∗$ be a star operation of finite character on $D$, $∗_w$ be the so-called $∗_w$-operation on $D$ induced by $∗$, $X$ be an indeterminate over $D$, $N_∗ = {f \in D[X]|c(f)^∗ = D}$, and $Kr(D, ∗) ={0} \bigcup {\frac{f}{g} |0 = f, g \in D[X] \mbox{and there is an }0 = h \in D[X] \mbox{such that } (c(f)c(h))∗ \subset (c(g)c(h))^∗}$. In this paper, we show that D is $a ∗$-quasi-Prufer domain if and only if $D[X]_{N_∗} = Kr(D, ∗_w)$. As a
corollary, we recover Fontana-Jara-Santos’s result that D is a Prufer ∗-multiplication domain if and only if $D[X]N∗ = Kr(D, ∗w )$.


Subject classification



Sponsor(s)



Full Text:

PDF

Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr