Special Issue "Algebra and Number Theory"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebraic Geometry".

Deadline for manuscript submissions: 31 July 2020.

Special Issue Editors

Prof. Michele Elia
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Guest Editor
Department of Electronic& Telecommunication, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Interests: Algebra; Number Theory; Information Theory; Cryptography
Prof. J. Carmelo Interlando
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Guest Editor
Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA.
Interests: Lattice Packings; Number Fields; Algebraic Coding Theory; Modulation Schemes; Cryptology and Algorithmic Complexity
Dr. Nadir Murru
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Guest Editor
Department of Mathematics G. Peano, University of Turin, Via Carlo Alberto 10, 10123, Torino, Italy
Interests: Mathematics; Algebra; Number Theory

Special Issue Information

Dear Colleagues,

Algebra and number theories have always attracted the human mind, stimulated man’s curiosity, and have significantly contributed to forging the mathematical disciplines that pervade every aspect of modern life. Although it is difficult to foresee the future domains of application of aimless pure mathematical discoveries, today’s dominating fields are information theory and cryptography.

The prophetic words of Abraham Adrian Albert, stating that “abstract cryptography is identical with abstract mathematics”, could not be truer today in view of the reliance of modern society on cryptography for connectivity and intelligent systems. The prophecy may have included fascinating branches and problems in algebra and number theory; in particular, those of a computational and combinatorial nature such as the following:

  • Finite fields
  • Generation of sequences with random characteristics and the study of their complexity
  • The intractability of standard lattice problems, such as the shortest vector and the closest vector problems
  • Non-associative algebraic structures
  • The intractability of the general decoding problem for linear codes
  • Pairings, isogenies, and arithmetic of elliptic curves
  • Integer factoring, distribution of primes, and primality proving

Recently, applications involving many of the above branches and problems have been emerging for potential use in post-quantum cryptography. Although this trend is in line with today’s credo in applicable mathematics, the most relevant aspects of algebra and number theory are ultimately their beauty and the satisfaction of the human spirit: Fermat’s Last Theorem is likely the most eloquent example of that.

Prof. Michele Elia
Prof. J. Carmelo Interlando
Dr. Nadir Murru
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Computational complexity
  • Cryptography
  • Diophantine equations
  • Elliptic curves
  • Lattices
  • Linear codes
  • Pseudorandom sequences.

Published Papers (1 paper)

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Research

Open AccessArticle
Magnifiers in Some Generalization of the Full Transformation Semigroups
Mathematics 2020, 8(4), 473; https://doi.org/10.3390/math8040473 - 30 Mar 2020
Abstract
An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup [...] Read more.
An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup of all transformations on a nonempty set X under the composition of functions, P = { X i i Λ } be a partition, and ρ be an equivalence relation on the set X. In this paper, we focus on the properties of magnifiers of the set T ρ ( X , P ) = { f T ( X ) ( x , y ) ρ , ( x f , y f ) ρ and X i f X i for all i Λ } , which is a subsemigroup of T ( X ) , and provide the necessary and sufficient conditions for elements in T ρ ( X , P ) to be left or right magnifiers. Full article
(This article belongs to the Special Issue Algebra and Number Theory)
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