Radical semistar operations

Abstract

We introduce and study the set of radical semistar operations of an integral domain D. We show that their set is a complete lattice that is the join-completion of the set of spectral semistar operations, and we characterize when every radical operation is spectral (under the hypothesis that D is rad-colon coherent). When D is a Prüfer domain such that every set of minimal prime ideals is scattered, we completely classify stable semistar operations.

Keywords:

• Scattered spaces
• semistar operations
• stable operations

2020 Mathematics Subject Classification:

• 13A15
• 13A18
• 13F05
• 13F30
• 13G05