Stability in Witt rings

Craven, Thomas C.

doi:10.1090/S0002-9947-1977-0424800-9

Stability in Witt rings
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by Thomas C. Craven

Trans. Amer. Math. Soc. 225 (1977), 227-242

DOI: https://doi.org/10.1090/S0002-9947-1977-0424800-9

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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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