Divisorial rings and Cox rings
نویسنده
چکیده
1 Preliminaries on monoids Definition 1.1. An Abelian monoid is a set with a binary, associative, and commutative operation which has a neutral element. It will often be called just a monoid in this manuscript because we will not deal with non-commutative monoids. A monoid M is called • finitely generated if there is a finite set of generators, or equivalently if there is a surjection of monoids N ↠M for some r. • integral, if a + z = b + z implies a = b, • fine, if it is finitely generated and integral. • saturated, if for all x ∈< M > (see definition below) with nx ∈ M for some n ∈ N>0 is follows that x ∈M . Abelian monoids form a category, denoted by [ Ab mon ]. 1.2. We have the adjunctions
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