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On knots in algebraic number theory.

open access: yesJournal für die reine und angewandte Mathematik (Crelles Journal), 1979
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Algebra and Algebraic Number Theory [PDF]

open access: possible, 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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Some of the next articles are maybe not open access.

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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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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Algebraic Number Theory

1991
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as ...
Martin J. Taylor, A. Fröhlich
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