Closure operations, Continuous valuations on monoids and Spectral spaces
Rings and Algebras
2018-11-06 v2 Commutative Algebra
Abstract
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.
Cite
@article{arxiv.1806.10386,
title = {Closure operations, Continuous valuations on monoids and Spectral spaces},
author = {Samarpita Ray},
journal= {arXiv preprint arXiv:1806.10386},
year = {2018}
}
Comments
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