Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The Nagata-Higman Theorem

The Nagata-Higman Theorem Acta Applicandae Mathematicae 21:185-192, 1990. 185 © 1990 Kluwer Academic Publishers. Printed in the Netherlands. Edward Formanek ThePennsylvaniaState University, UniversityPark, PA 16802, U.S.A. This article is devoted to a history of the Nagata-Higman Theorem and related developments. The presentation is for the most part in chronological order, with one important exception. Approximately five years ago, Gerald Schwarz discovered that the Nagata-Higman Theorem had been proved by Dubnov and Ivanov [2] in 1943, nine years before the paper of Nagata. It had been completely overlooked by the mathematical community and had had no impact on subsequent research. Therefore in my history it appears as a recent archaeological find. The theorem proved by Nagata [5] in 1952 is Theorem I. Let A be an algebra over a field K of characteristic zero. Suppose that there is a positive integer n such that a n = 0 for all a ~ A . Then there is an integer N such that ala2...a N = 0 for all al,...,a N E A . By an algebra over K we mean an associative ring, not necessarily with a unit, with an action of K which commutes with the ring multiplication. It is apparent that http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

The Nagata-Higman Theorem

Formanek, Edward
Acta Applicandae Mathematicae , Volume 21 (2) – May 7, 2004
Download PDF
8 pages

Loading next page...
 
/lp/springer-journals/the-nagata-higman-theorem-8ywAdJ80G6

References (8)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00053297
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 21:185-192, 1990. 185 © 1990 Kluwer Academic Publishers. Printed in the Netherlands. Edward Formanek ThePennsylvaniaState University, UniversityPark, PA 16802, U.S.A. This article is devoted to a history of the Nagata-Higman Theorem and related developments. The presentation is for the most part in chronological order, with one important exception. Approximately five years ago, Gerald Schwarz discovered that the Nagata-Higman Theorem had been proved by Dubnov and Ivanov [2] in 1943, nine years before the paper of Nagata. It had been completely overlooked by the mathematical community and had had no impact on subsequent research. Therefore in my history it appears as a recent archaeological find. The theorem proved by Nagata [5] in 1952 is Theorem I. Let A be an algebra over a field K of characteristic zero. Suppose that there is a positive integer n such that a n = 0 for all a ~ A . Then there is an integer N such that ala2...a N = 0 for all al,...,a N E A . By an algebra over K we mean an associative ring, not necessarily with a unit, with an action of K which commutes with the ring multiplication. It is apparent that

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: May 7, 2004

There are no references for this article.