Closure operations, Continuous valuations on monoids and Spectral spaces
| Autor: | Samarpita Ray |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
13A15 13A18 13B22 54D80 Algebra and Number Theory Applied Mathematics Closure operation 010102 general mathematics Closure (topology) Mathematics - Rings and Algebras Type (model theory) Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Rings and Algebras (math.RA) Mathematics::Category Theory 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Commutative algebra Mathematics |
| DOI: | 10.48550/arxiv.1806.10386 |
| Popis: | We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in this work. In the process, we make a detailed study of different closure operations on monoids. We prove that the collection of continuous valuations on a topological monoid with topology determined by any finitely generated ideal is a spectral space. Comment: 20 pages; typos corrected; added references; added examples in section 5.2; few revised arguments in section 5.1 but results unchanged; Proposition 5.3 added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|