Galois theory of continuous transformation rings
نویسندگان
چکیده
منابع مشابه
Generalized affine transformation monoids on Galois rings
Let A be a ring with identity. The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form x → xu + a (for all x ∈ A), where u,a∈ A. We study the algebraic structure of the monoid Gaff(A) on a finite Galois ring A. The following results are obtained: an explicit description of Green’s relations on Gaff(A); and an explicit description of the...
متن کاملOn the Galois Theory of Division Rings
1. Throughout this paper, K will represent a division ring and L a galois division subring. We are interested in establishing a galois theory for the extension K/L when K/L is locally finite. In order to do this one must identify the galois subrings of K containing L. An example given by Jacobson [4] shows that not every such division subring is galois. However, we obtain that each subring subj...
متن کاملGalois Theory and Integral Models of Λ-rings
We show that any Λ-ring, in the sense of Riemann–Roch theory, which is finite étale over the rational numbers and has an integral model as a Λ-ring is contained in a product of cyclotomic fields. In fact, we show that the category of them is described in a Galois-theoretic way in terms of the monoid of pro-finite integers under multiplication and the cyclotomic character. We also study the maxi...
متن کاملGeneralized Rings of Measurable and Continuous Functions
This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.
متن کاملSchur rings over a product of Galois rings
The recently developed theory of Schur rings over a finite cyclic group is generalized to Schur rings over a ring R being a product of Galois rings of coprime characteristics. It is proved that if the characteristic of R is odd, then as in the cyclic group case any pure Schur ring over R is the tensor product of a pure cyclotomic ring and Schur rings of rank 2 over non-fields. Moreover, it is s...
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: Transactions of the American Mathematical Society
سال: 1955
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1955-0072121-4