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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extensions of difference specializations


Author: Barbara Lando
Journal: Proc. Amer. Math. Soc. 79 (1980), 197-202
MSC: Primary 12H10; Secondary 13J99, 13N05
DOI: https://doi.org/10.1090/S0002-9939-1980-0565337-1
MathSciNet review: 565337
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Abstract: Maximal difference specializations and difference places are defined. Let R be the domain of a difference specialization $ \phi $ of a difference field K and $ x \in K$. Then $ \phi $ can be extended to a specialization $ x \to 0$ if and only if $ 1 \notin [x]$. This result applies to give a condition on a polynomial for the extension of a specialization to its generic zero. In a slightly different direction, a necessary and sufficient condition for the extension of a specialization to a larger difference field is given.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0565337-1
Keywords: Difference specialization, difference place, maximal difference ring
Article copyright: © Copyright 1980 American Mathematical Society