On semisimple extensions and separable extensions over non commutative rings
نویسندگان
چکیده
منابع مشابه
On Separable Abelian Extensions of Rings
Let R be a ring with I, G (= (1>x...Xm) a finite abelian automorphism group of R of order n where (i2 is cyclic of order n. for some integers n, hi, and m, and C the center of R whose automorphism group induced by G is isomorphic with G. Then an abelian extension Rtx 1,...,xm is defined as a generalization of cyclic extensions of rings, and RXl,...,Xm is an Azumaya algebra over K (= CG {c in C ...
متن کاملGalois Extensions over Commutative and Non-commutative Base
This paper is a written form of a talk. It gives a review of various notions of Galois (and in particular cleft) extensions. Extensions by coalgebras, bialgebras and Hopf algebras (over a commutative base ring) and by corings, bialgebroids and Hopf algebroids (over a non-commutative base algebra) are systematically recalled and compared. In the first version of this paper, the journal version o...
متن کاملSeparable Algebras over Commutative Rings
Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...
متن کاملCommutative Regular Rings without Prime Model Extensions
It is known that the theory K of commutative regular rings with identity has a model completion K . We show that there exists a countable model of K which has no prime extension to a model of K'. If K and K ate theories in a first order language L, then K is said to be a model completion of K if K extends K, every model of K can be embedded in a model of K , and for any model A of K and models ...
متن کاملOn Some Properties of Extensions of Commutative Unital Rings
Throughout the text, let R be a commutative ring with identity (often called a commutative unital ring) and with multiplicative group of units R∗. Likewise, let f(x) = a0x +a1x n−1+ · · ·+an−1x+an be a polynomial of the variable x over R such that a0 ∈ R∗. Traditionally, R[x] is the ring of all polynomials of x over R; thereby f(x) ∈ R[x]. For an arbitrary but fixed element α, suppose f(x) is t...
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: 1966
ISSN: 0025-5645
DOI: 10.2969/jmsj/01840360