Coherence and weak factoriality in a certain pullback

Abstract

Let D be a domain with its quotient field K. Let $K[\theta ]=K[x]/(x^n)$ where x is an indeterminate and $\theta =x+(x^n)$. Denote by $R_n=D+\theta K[\theta ]$, which is a subring of $K[\theta ]$. This paper studies several properties of R_n: coherence, weakly factorial rings, strong Mori rings, rings with Noetherian spectrum, weak normality, and t-closedness.

KEYWORDS:

• Coherent ring
• Noetherian spectrum
• pullback construction
• quasi-coherent ring
• seminormal
• strong Mori ring
• (strongly) t-closed
• v-coherent ring
• w-coherent ring
• weakly factorial ring
• weakly normal

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13A15
• 13F05

Acknowledgments

The authors would like to thank the reviewer for his/her comments and suggestions, which led to the improvement of the paper.

Additional information

Funding

This research was supported by the Academic Research Fund of Hoseo University in 2020 (20200812).