A correspondence between irregular fields
- Creators
- Bell, E. T.
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.
Additional Information
© 1930 American Mathematical Society. Presented to the Society, April 5, 1930.Additional details
- Eprint ID
- 102410
- Resolver ID
- CaltechAUTHORS:20200408-151234457
- Created
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2020-04-08Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field