منابع مشابه
A new criterion on normal bases of finite field extensions
A new criterion on normal bases of finite field extension Fqn/Fq is presented and explicit criterions for several particular finite field extensions are derived from this new criterion.
متن کاملGröbner Bases Applied to Finitely Generated Field Extensions
Let k(~x) := k(x1, . . . , xn) be a finitely generated extension field of some field k, and denote by k(~g) := k(g1, . . . , gr) an intermediate field of k(~x)/k generated over k by some elements g1, . . . , gr ∈ k(~x). So geometrically, we may take ~g for rational functions on the variety determined by the generic point (~x). To determine whether the extension k(~x)/k(~g) is transcendental or ...
متن کاملGröbner-Shirshov bases for extensions of algebras
An algebra R is called an extension of the algebra M by B if M = 0, M is an ideal of R and R/M ∼= B as algebras. In this paper, by using the Gröbner-Shirshov bases, we characterize completely the extensions of M by B. An algorithm to find the conditions of an algebra A to be an extension of M by B is obtained.
متن کامل(Pure) transcendence bases in $\phi$-deformed shuffle bialgebras
Computations with integro-differential operators are often carried out in an associative algebra with unit and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators perform on a bialgebra isomorphic to an enveloping algebra. That gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure)...
متن کاملFinitary Galois Extensions over Noncommutative Bases
We study Galois extensions M (co-)H ⊂ M for H-(co)module algebras M if H is a Frobenius Hopf algebroid. The relation between the action and coaction pictures is analogous to that found in Hopf-Galois theory for finite dimensional Hopf algebras over fields. So we obtain generalizations of various classical theorems of Kreimer-Takeuchi, Doi-Takeuchi and Cohen-FischmanMontgomery. We find that the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1982
ISSN: 0025-5645
DOI: 10.2969/jmsj/03440703