Korean J. Math.  Vol 22, No 4 (2014)  pp.591-598
DOI: https://doi.org/10.11568/kjm.2014.22.4.591

Finitely $t$-valuative domains

Gyu Whan Chang


Let $D$ be an integral domain with quotient field $K$. In \cite{cdl12}, the authors called $D$ a finitely valuative domain if, for each $0 \neq u \in K$, there is a saturated chain of rings $D = D_0 \subsetneq D_1 \subsetneq \cdots D_n = D[x]$, where $x = u$ or $u^{-1}$. They then studied some properties of finitely valuative domains. For example, they showed that the integral closure of a finitely valuative domain is a Pr\"ufer domain. In this paper, we introduce the notion of finitely $t$-valuative domains, which is the $t$-operation analog of finitely valuative domains, and we then generalize some properties of finitely valuative domains.


Finitely $t$-valuative domain, P$v$MD, $t$-operation

Subject classification



This work was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0007069).

Full Text:



P.-J. Cahen, D.E. Dobbs, and T.G. Lucas, Finitely valuative domains, J. Algebra Appl. 6 (2012), 1250112 (39 pages). (Google Scholar)

G.W. Chang, Strong Mori domains and the ring D[X]Nv , J. Pure Appl. Algebra 197 (2005), 293–304. (Google Scholar)

G.W. Chang, Overrings of the Kronecker function ring Kr(D,∗) of a Pru ̈fer ∗-multiplication domain D, Bull. Korean Math. Soc. 46 (2009), 1013–1018. (Google Scholar)

G.W. Chang and M. Fontana, Upper to zero in polynomial rings and Pru ̈fer-like (Google Scholar)

domains, Comm. Algebra 37 (2009), 164–192. (Google Scholar)

M. Fontana, S. Gabelli, and E. Houston, UMT-domains and domains with Pru ̈fer (Google Scholar)

integral closure, Comm. Algebra 26 (1998), 1017–1039. (Google Scholar)

E. Houston and M. Zafrullah, On t-invertibility II, Comm. Algebra 17 (1989), 1955–1969. (Google Scholar)

B.G. Kang, Pru ̈fer v-multiplication domains and the ring R[X]Nv , J. Algebra 123 (1989), 151–170. (Google Scholar)


  • 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