Displaying similar documents to “Manis valuations and Prüfer extensions. I.”

Algebraic Numbers

Yasushige Watase (2016)

Formalized Mathematics

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This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to...

Commutative algebraic groups and p-adic linear forms

Clemens Fuchs, Duc Hiep Pham (2015)

Acta Arithmetica

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Let G be a commutative algebraic group defined over a number field K that is disjoint over K from a and satisfies the condition of semistability. Consider a linear form l on the Lie algebra of G with algebraic coefficients and an algebraic point u in a p-adic neighbourhood of the origin with the condition that l does not vanish at u. We give a lower bound for the p-adic absolute value of l(u) which depends up to an effectively computable constant only on the height of the linear form,...