arXiv Open Access 2025

The Japanese and universally Japanese properties for valuation rings and Prüfer domains

Shiji Lyu

Lihat Sumber

Abstrak

We discuss the Japanese and universally Japanese properties for valuation rings and Prüfer domains. These properties, regarding finiteness of integral closure, have been studied extensively for Noetherian rings, but very rarely, if ever, for non-Noetherian rings. Among other results, we show that for valuation rings and Prüfer domains, the Japanese and universally Japanese properties are equivalent. This result can be seen as a counterpart to Nagata's classical result for Noetherian rings. This result also tells us many non-Noetherian rings, including all absolutely integrally closed valuation rings and Prüfer domains, are universally Japanese.

Topik & Kata Kunci

math.AC

Penulis (1)

Shiji Lyu

Format Sitasi

APA MLA BibTeX

Lyu, S. (2025). The Japanese and universally Japanese properties for valuation rings and Prüfer domains. https://arxiv.org/abs/2502.12357

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓