On injectivity of natural homomorphisms of witt rings
Abstract
We study the homomorphism W𝓞 → WK between the Witt ring of a domain 𝓞 and the Witt ring of its field of fractions K in the case when 𝓞 is not integrally closed. We give sufficient conditions for the noninjectivity of this homomorphism by constructing nonzero elements in the kernel. In particular, when K is an algebraic number field and 𝓞 is a nonmaximal order in K with even conductor, then the ring homomorphism W𝓞 → WK is not injective.
Keywords
Witt ring; order in a number field
References
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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