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IX.—On a Certain Variation of the Distributive Law for a Commutative Algebraic Field

Published online by Cambridge University Press:  14 February 2012

Abraham Robinsohn
Abraham Robinsohn
Affiliation:
Hebrew University of Jerusalem
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Summary

A quasi-field is denned by the postulates of a commutative algebraic field, except that the distributive law a(b + c) = ab + ac is replaced by a(b1+ … +bn)=ab1+ … +abn for a fixed integer n.

The properties of quasi-fields are investigated. The study of their ideals is reduced to the study of the ideals of a certain type of ring. A particular quasi-field is constructed formally by means of polynomial domains modulo a natural number, with addition specially defined.

Quasi-fields are connected with multiple fields—another generalisation of the conception of a commutative field, in which a fixed number of elements (> 2) co-operate symmetrically in the formation of any sum or product.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 61 , Issue 1 , 1941 , pp. 93 - 101
Copyright
Copyright © Royal Society of Edinburgh 1941

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References

References to Literature

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