Bell, E. T. (1930) A correspondence between irregular fields. Bulletin of the American Mathematical Society, 36 (6). pp. 415-419. ISSN 0002-9904. doi:10.1090/s0002-9904-1930-04961-7. 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 | ||||||
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Related URLs: |
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Additional Information: | © 1930 American Mathematical Society. Presented to the Society, April 5, 1930. | ||||||
Issue or Number: | 6 | ||||||
DOI: | 10.1090/s0002-9904-1930-04961-7 | ||||||
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: | 16 Nov 2021 18:11 |
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