Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2018; 55(4): 1093-1101

Online first article March 8, 2018      Printed July 31, 2018

https://doi.org/10.4134/BKMS.b170600

Copyright © The Korean Mathematical Society.

Pullbacks of $\mathcal{C}$-hereditary domains

Yongyan Pu, Gaohua Tang, Fanggui Wang

Panzhihua University, Guangxi Teacher's Education University, Sichuan Normal University

Abstract

Let $(RDTF,M)$ be a Milnor square. In this paper, it is proved that $R$ is a $\mathcal{C}$-hereditary domain if and only if both $D$ and $T$ are $\mathcal{C}$-hereditary domains; $R$ is an almost perfect domain if and only if $D$ is a field and $T$ is an almost perfect domain; $R$ is a Matlis domain if and only if $T$ is a Matlis domain. Furthermore, to give a negative answer to Lee$^,$s question, we construct a counter example which is a $\mathcal{C}$-hereditary domain $R$ with $w.gl.\dim(R)=\infty$.

Keywords: $\mathcal{C}$-hereditary domain, Matlis domain, almost perfect domain, Milnor square

MSC numbers: 13C99, 13A15

Stats or Metrics

Share this article on :

Related articles in BKMS