Benutzer:Monoeed/almostring
Aus der englischen Wikipedia:
In mathematics, almost rings are the analogues of commutative rings in the "almost mathematics" introduced by harvs 1988 in his study of p-adic Hodge theory. Roughly speaking, the word "almost" means "ignore m-torsion for a certain idempotent ideal m".
Definition
Suppose that V is a ring and m an ideal such that m2 = m and m ⊗ m is a flat V-module. An almost V module is an element of the category of V-modules modulo the full subcategory of modules killed by m; these form a tensor abelian category. An almost ring (or more precisely an almost V-algebra) is an almost V-module with a bilinear multiplication map satisfying some conditions similar to the axioms for a ring.
Example
In the original paper by Faltings, V was the integral closure of a discrete valuation ring in the algebraic closure of its quotient field, and m its maximal ideal.
References
- Faltings|first= Gerd|authorlink=Gerd Faltings|title=p-adic Hodge theory
|journal=J. Amer. Math. Soc.|volume= 1 |year=1988|issue= 1|pages= 255–299|doi=10.2307/1990970
- Gabber|first=Ofer|last2= Ramero|first2= Lorenzo
|title=Almost ring theory|series=Lecture Notes in Mathematics|volume= 1800|publisher= Springer-Verlag|place= Berlin|year= 2003|isbn= 3-540-40594-1|doi=10.1007/b10047
