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Index, sub-index and sub-factor of groups with interactions to number theory
Journal of Algebra and its Applications, 2020This paper is the first step of a new topic about groups which has close relations and applications to number theory. Considering the factorization of a group into a direct product of two subsets, and since every subgroup is a left and right factor, we ...
M. Hooshmand
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Applied Algebra and Number Theory
, 2014Preface Gerhard Larcher, Friedrich Pillichshammer, Arne Winterhof and Chaoping Xing 1. Some highlights of Harald Niederreiter's work Gerhard Larcher, Friedrich Pillichshammer, Arne Winterhof and Chaoping Xing 2.
H. Niederreiter +4 more
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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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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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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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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, 1952in 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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, 1986
Found opportunities Classical special functions and L. J. Rogers W. N. Bailey's extension of Roger's work Constant terms Integrals Partitions and $q$-series Partitions and constant terms The hard hexagon model Ramanujan Computer algebra Appendix A.
G. Andrews
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Found opportunities Classical special functions and L. J. Rogers W. N. Bailey's extension of Roger's work Constant terms Integrals Partitions and $q$-series Partitions and constant terms The hard hexagon model Ramanujan Computer algebra Appendix A.
G. Andrews
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Learning number theory with a computer algebra system
, 1996The paper discusses how a computer algebra system MAPLE can be used to enhance the learning of concepts, theorems and algorithms in an elementary classical number theory course. There are 20 built‐in routines selected from the MAPLE number theory package
Y. L. Cheung
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Algebraic properties of number theories
Israel Journal of Mathematics, 1975Among other things we prove the following. (A) A number theory is convex if and only if it is inductive. (B) No r.e. number theory has JEP. (C) No number theory has AP. We also give some information about the hard cores of number theories.
H. Simmons +3 more
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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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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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JP Journal of Algebra Number Theory and Applications, 2018
D. Gómez-Ramírez +4 more
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D. Gómez-Ramírez +4 more
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