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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Finitely generated extensions of partial difference fields


Author: Peter Evanovich
Journal: Trans. Amer. Math. Soc. 281 (1984), 795-811
MSC: Primary 12H10; Secondary 12F99
MathSciNet review: 722775
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Abstract: A proof of the following theorem is given: If $ \mathcal{M}$ is a finitely generated extension of a partial difference field $ \mathcal{K}$ then every subextension of $ \mathcal{M}/\mathcal{K}$ is finitely generated. An integral measure of partial difference field extensions having properties similar to the dimension of field extensions and the limit degree of ordinary difference field extensions and a new method of computing transformal transcendence degree are developed.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0722775-X
Keywords: Partial difference field, finitely generated partial difference field extensions, limit degree, transformally algebraically independent, transformal transcendence degree
Article copyright: © Copyright 1984 American Mathematical Society