منابع مشابه
On 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 کاملOrderings for Noncommutative Rings
Introduction and Notation. The goal of this paper is to present the beginnings of a theory of real algebraic geometry for noncommutative rings. For a basic introduction to the commutative theory, see Lam [L]. The word field will be used in this paper to mean a (generally noncommutative) skewfield; we shall specify a commutative field when we need to. R will denote a noncommutative ring with 1. ...
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 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 کاملThe Quest for Quotient Rings (Of Noncommutative Noetherian Rings)
Articles on the history of mathematics can be written from many different perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop and movements are born or become obsolete. At the other extreme, there are those that try to shed light on the history of particular theorems and on the people who created them. This article belo...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1967
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1967-0215883-3