Abstract
Let R be a domain. It is proved that R is coherent when IF D(R) ≤ 1, and R is Noetherian when IP D(R) ≤ 1. Consequently, R is a G-Prüfer domain if and only if IF D(R) ≤ 1, if and only if wG-gldim(R) ≤ 1; and R is a G-Dedekind domain if and only if IP D(R) ≤ 1.
| Original language | English |
|---|---|
| Pages (from-to) | 1075-1081 |
| Number of pages | 7 |
| Journal | Bulletin of the Korean Mathematical Society |
| Volume | 57 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2020 |
Keywords
- G-Prüfer domain
- IF D(R)
- IP D(R)
- wG-gldim(R)