A Historical Perspective of the Theory of Isotopisms

In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide...

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Main Authors:	Raúl M. Falcón, Óscar J. Falcón, Juan Núñez
Format:	Article
Language:	English
Published:	MDPI AG 2018-08-01
Series:	Symmetry
Subjects:	isotopism classification non-associative algebra quasigroup Latin square
Online Access:	http://www.mdpi.com/2073-8994/10/8/322

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spelling	doaj-e76270b044564c1caeda01010630686a2020-11-24T22:22:37ZengMDPI AGSymmetry2073-89942018-08-0110832210.3390/sym10080322sym10080322A Historical Perspective of the Theory of IsotopismsRaúl M. Falcón0Óscar J. Falcón1Juan Núñez2Department Applied Mathematics I, University of Sevilla, 41004 Seville, SpainDepartment Geometry and Topology, University of Sevilla, 41004 Seville, SpainDepartment Geometry and Topology, University of Sevilla, 41004 Seville, SpainIn the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the literature concerning the classification and enumeration of different algebraic and combinatorial structures according to their isotopism classes. In spite of that, there does not exist any contribution dealing with the origin and development of such a theory. This paper is a first approach in this regard.http://www.mdpi.com/2073-8994/10/8/322isotopismclassificationnon-associative algebraquasigroupLatin square
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Raúl M. Falcón Óscar J. Falcón Juan Núñez
spellingShingle	Raúl M. Falcón Óscar J. Falcón Juan Núñez A Historical Perspective of the Theory of Isotopisms Symmetry isotopism classification non-associative algebra quasigroup Latin square
author_facet	Raúl M. Falcón Óscar J. Falcón Juan Núñez
author_sort	Raúl M. Falcón
title	A Historical Perspective of the Theory of Isotopisms
title_short	A Historical Perspective of the Theory of Isotopisms
title_full	A Historical Perspective of the Theory of Isotopisms
title_fullStr	A Historical Perspective of the Theory of Isotopisms
title_full_unstemmed	A Historical Perspective of the Theory of Isotopisms
title_sort	historical perspective of the theory of isotopisms
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2018-08-01
description	In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the literature concerning the classification and enumeration of different algebraic and combinatorial structures according to their isotopism classes. In spite of that, there does not exist any contribution dealing with the origin and development of such a theory. This paper is a first approach in this regard.
topic	isotopism classification non-associative algebra quasigroup Latin square
url	http://www.mdpi.com/2073-8994/10/8/322
work_keys_str_mv	AT raulmfalcon ahistoricalperspectiveofthetheoryofisotopisms AT oscarjfalcon ahistoricalperspectiveofthetheoryofisotopisms AT juannunez ahistoricalperspectiveofthetheoryofisotopisms AT raulmfalcon historicalperspectiveofthetheoryofisotopisms AT oscarjfalcon historicalperspectiveofthetheoryofisotopisms AT juannunez historicalperspectiveofthetheoryofisotopisms
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A Historical Perspective of the Theory of Isotopisms

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