Titlebook: Kähler Differentials; Ernst Kunz Book 1986 Springer Fachmedien Wiesbaden 1986 Algebra.Endlichkeit.Funktion.Variable.differential algebra.p

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Regularity Criteria for Semianalytic Algebras,al ring whose maximal ideal is generated by p•1, where p is the characteristic of the residue field of k. Let S be a semianalytic k-algebra, and let R be an analytic k-algebra such that S is essentially of finite type over R. Being a complete semi-local noetherian ring, R is universally catenary, hence for ℘, ℘′ ∈ Spec(S) with ℘ ⊂ ℘ we have ..

Carminative

Existence of p-Bases,say that a . S ⊃ R ⊃ S. is given. In this case S/R is also a finitely presented algebra (that is, there is a presentation S = R[X., ..., X.]/I with a finitely generated ideal I of R[X., ..., X.]), and Ω. is a finitely presented S-module.

NEEDY

Abjure

掺假

Morphine

Living-Will

0932-7134 Overview: 978-3-528-08973-3978-3-663-14074-0Series ISSN 0932-7134 Series E-ISSN 2512-7039

单纯

Derivations,In this section we shall discuss the notion of derivation. Some examples of derivations are given, and some basic rules about derivations are proved. Important invariants of an algebra are its derivation module and its module of (Kahler) differentials, which will be introduced at the end of this section.

挑剔为人

Differential Algebras,A method to study algebras is to study their differential algebras. This notion, which is analogous to the notion of the algebra of differential forms in analysis, will be introduced here and some of its basic properties will be established.

歌唱队

Universal Extension of a Differential Algebra,We first prove the existence of a “universal” differential algebra of R/R., of which any other differential algebra of R/R. is a homomorphic image. Later the notion of universal differential algebra will be generalized to that of a “universal extension” of a differential algebra.