Results 281 to 290 of about 600,804 (334)

ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS

Mathematics of the USSR-Sbornik, 1985
This paper contains a complete proof of the following theorem. Let \(\alpha\neq 0,1\) be algebraic, let \(\beta\) be algebraic of degree \(d\geq 2\), and let t be the transcendence degree over \({\mathbb{Q}}\) of the field generated by the numbers (*) \(\alpha^{\beta},...,\alpha^{\beta^{d- 1}}\).
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Algebra and Algebraic Number Theory

1992
The 19th century was an age of deep qualitative transformations and, at the same time, of great discoveries in all areas of mathematics, including algebra. The transformation of algebra was fundamental in nature. Between the beginning and the end of the last century, or rather between the beginning of the last century and the twenties of this century ...
I. G. Bashmakova, A. N. Rudakov
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Algebraic numbers

1998
Abstract Many important numbers, such as ../2 and i, are solutions of polynomial equations. Such numbers are said to be algebraic, and we shall study their basic theory in this chapter. Algebraic numbers also occur frequently in the following context: We start with a polynomial f(X) over Q and we wish to study the solutions of the ...
A W Chatters, C R Hajarnavis
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Random Algebraic Numbers

Journal of Mathematical Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Realizing Algebraic Number Fields

1983
In the paper [13], the authors studied the problem of realizing rational division algebras in a special way. Let D be a division algebra that is finite dimensional over the rational field Q. If p is a prime, we say that D is p-realizable when there is a p-local torsion free abelian group A whose rank is the dimension of D over Q, such that D is ...
R. S. Pierce, C. I. Vinsonhaler
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Algebraic Numbers and Algebraic Functions

1991
Part 1 Fields with valuations: absolute values the topology defined by an absolute value complete fields valuations, valuation rings and places the representation by power series ordered groups general valuations. Part 2 Extensions: generalities on extensions extensions of complete fields extensions of incomplete fields Dedekind domains and the string ...
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Hypercomplex Numbers: From Algebra to Algebras

2015
The term “algebra” dates back to the ninth century AD, but the subject, referring to the solution of polynomial equations, is roughly four thousand years old. It originated in about 1800 BC, with the Babylonians, who solved linear and quadratic equations much as we do today.
Hardy Grant, Israel Kleiner
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RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS

Mathematics of the USSR-Izvestiya, 1971
In this article we derive a new effective estimate of rational approximations to algebraic numbers simultaneously in an Archimedian and several non-Archimedian metrics.
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Algebraic Number Theory

2021
This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number
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A Weil Banach Algebra for Multiplicative Algebraic Numbers

Journal of Number Theory, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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