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A correspondence between irregular fields

Bell, E. T. (1930) A correspondence between irregular fields. Bulletin of the American Mathematical Society, 36 (6). pp. 415-419. ISSN 0002-9904. https://resolver.caltech.edu/CaltechAUTHORS:20200408-151234457

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Abstract

Correspondences between fields are well known, and Dickson has applied one to obtain a generalization of the theory of numbers. Here we give an instance of correspondence between irregular fields. An irregular field differs from a field only in the exclusion of an infinity of elements as divisors, instead of the uniquely excluded zero of a field. The postulates for an irregular field and numerous instances were given elsewhere. The correspondence is established between the irregular field of all numerical functions and the irregular field of a certain infinity of power series with radius of convergence 1. For the series considered, addition and subtraction are interpreted as in the classical algebra of absolutely convergent series; multiplication and division receive wholly different interpretations. The simplest instance of the new multiplication is the process by which, when legitimate, a Lambert series is derived from a given power series.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/s0002-9904-1930-04961-7DOIArticle
Additional Information:© 1930 American Mathematical Society. Presented to the Society, April 5, 1930.
Issue or Number:6
Record Number:CaltechAUTHORS:20200408-151234457
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200408-151234457
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102410
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Apr 2020 23:03
Last Modified:08 Apr 2020 23:03

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