Results 261 to 270 of about 635,864 (319)

Enhancing energy predictions in multi-atom systems with multiscale topological learning.

J Mater Chem A Mater
Chen D, Wang R, Wei GW, Pan F.
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The Roots of Commutative Algebra in Algebraic Number Theory

Mathematics Magazine, 1995
To put the issues in a broader context, these three number-theoretic problems were instrumental in the emergence of algebraic number theory-one of the two main sources of the modern discipline of commutative algebra.' The other source was algebraic geometry.
I. Kleiner
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Algebraic Number Theory

1986
S. Lang
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Introduction to Algebraic Number Theory [PDF]

, 1982
By an algebraic number we mean a number 9 which is a root of the algebraic equation $$f(x) = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_0 = 0,$$ (1)
H. Keng
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Algebra and Algebraic Number Theory [PDF]

, 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 Number Theory, Second Edition

, 2011
Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation.
R. Mollin
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Algebraic Number Theory

1982
In this chapter we shall introduce the concept of an algebraic number field and develop its basic properties. Our treatment will be classical, developing directly only those aspects that will be needed in subsequent chapters. The study of these fields, and their interaction with other branches of mathematics forms a vast area of current research.
Kenneth Ireland, Michael Rosen
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Introductory Algebraic Number Theory

, 2003
Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and ...
S. Alaca, K. Williams
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Algebra and Number Theory

2002
Public-key cryptosystems are based on modular arithmetic. In this section, we summarize the concepts and results from algebra and number theory which are necessary for an understanding of the cryptographic methods. Textbooks on number theory and modular arithmetic include [HarWri79], [IreRos82], [Rose94], [Forster96] and [Rosen2000].
Helmut Knebl, Hans Delfs
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A Development of Associative Algebra and an Algebraic Theory of Numbers, I

Mathematics Magazine, 1952
in which if we denote a particular element by Ck, its immediate successor in this is CkJ, where k denotes a natural number and k' its immediate successor in the set of natural numbers. We then introduced in addition to these symbols the symbol + (called a plus sign); x (called a multiplication sign); and (, called a left parenthesis symbol; and ...
M. W. Weaver, H. S. Vandiver
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