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

Abstract


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.

Keywords


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

Subject classification

13A15

Sponsor(s)

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).

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