Traduction et analyse de mots par intelligence artificielle ChatGPT
Sur cette page, vous pouvez obtenir une analyse détaillée d'un mot ou d'une phrase, réalisée à l'aide de la meilleure technologie d'intelligence artificielle à ce jour:
- comment le mot est utilisé
- fréquence d'utilisation
- il est utilisé plus souvent dans le discours oral ou écrit
- options de traduction de mots
- exemples d'utilisation (plusieurs phrases avec traduction)
- étymologie
quasi-ring - traduction vers russe
общая лексика
квазикольцо
неассоциативное кольцо
![[[Richard Dedekind]], one of the founders of [[ring theory]].](https://commons.wikimedia.org/wiki/Special:FilePath/Dedekind.jpeg?width=200 "[[Richard Dedekind]], one of the founders of [[ring theory]].")
![The [[integer]]s, along with the two operations of [[addition]] and [[multiplication]], form the prototypical example of a ring.](https://commons.wikimedia.org/wiki/Special:FilePath/Number-line.svg?width=200 "The [[integer]]s, along with the two operations of [[addition]] and [[multiplication]], form the prototypical example of a ring.")
математика
унитарная алгебра
Définition
Wikipédia
In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is called an excellent ring if it is also universally catenary. Excellent rings are one answer to the problem of finding a natural class of "well-behaved" rings containing most of the rings that occur in number theory and algebraic geometry. At one time it seemed that the class of Noetherian rings might be an answer to this problem, but Masayoshi Nagata and others found several strange counterexamples showing that in general Noetherian rings need not be well-behaved: for example, a normal Noetherian local ring need not be analytically normal.
The class of excellent rings was defined by Alexander Grothendieck (1965) as a candidate for such a class of well-behaved rings. Quasi-excellent rings are conjectured to be the base rings for which the problem of resolution of singularities can be solved; Hironaka (1964) showed this in characteristic 0, but the positive characteristic case is (as of 2016) still a major open problem. Essentially all Noetherian rings that occur naturally in algebraic geometry or number theory are excellent; in fact it is quite hard to construct examples of Noetherian rings that are not excellent.
