Picard Groups and Class Groups of Monoid Schemes
arXiv:1306.4928 · doi:10.1016/j.jalgebra.2014.06.002
Abstract
We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations. The normalization of a monoid turns out to be a monoid scheme, but not always a monoid.
14 pages