Abstract
Let D be an integral domain, ∗ a star-operation on D, and S a multiplicative subset of D. We define D to be an S-∗w-principal ideal domain if for each nonzero ideal I of D, there exist an element s S and a principal ideal (c) of D such that ∪(c)∪I∗w. In this paper, we study some properties of S-∗w-principal ideal domains. Among other things, we study the local property, the Nagata type theorem, and the Cohen type theorem for S-∗w-principal ideal domains.
| Original language | English |
|---|---|
| Pages (from-to) | 217-224 |
| Number of pages | 8 |
| Journal | Algebra Colloquium |
| Volume | 25 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Jun 2018 |
Keywords
- S -∗ -principal
- S -∗ -principal ideal domain
- ∗ -Dedekind domain
- ∗-countable type