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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stability in Witt rings


Author: Thomas C. Craven
Journal: Trans. Amer. Math. Soc. 225 (1977), 227-242
MSC: Primary 13K05; Secondary 13A15
MathSciNet review: 0424800
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Abstract: An abstract Witt ring R is defined to be a certain quotient of an integral group ring for a group of exponent 2. The ring R has a unique maximal ideal M containing 2. A variety of results are obtained concerning n-stability, the condition that $ {M^{n + 1}} = 2{M^n}$, especially its relationship to the ring of continuous functions from the space of minimal prime ideals of R to the integers. For finite groups, a characterization of integral group rings is obtained in terms of n-stability. For Witt rings of formally real fields, conditions equivalent to n-stability are given in terms of the real places defined on the field.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0424800-9
PII: S 0002-9947(1977)0424800-9
Keywords: Witt ring, n-stability, group ring, real place, Boolean space
Article copyright: © Copyright 1977 American Mathematical Society