CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS

The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various varieties of algebras, such as Lie, Leibniz and Malcev algebras....

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Autores:
GUTIERREZ, I. S.
Tipo de recurso:
Fecha de publicación:
2020
Institución:
Universidad del Atlántico
Repositorio:
Repositorio Uniatlantico
Idioma:
eng
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oai:repositorio.uniatlantico.edu.co:20.500.12834/891
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https://hdl.handle.net/20.500.12834/891
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dc.title.spa.fl_str_mv CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
title CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
spellingShingle CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
title_short CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
title_full CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
title_fullStr CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
title_full_unstemmed CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
title_sort CLASSES OF ALGEBRAS AND CLOSURE OPERATIONS
dc.creator.fl_str_mv GUTIERREZ, I. S.
dc.contributor.author.none.fl_str_mv GUTIERREZ, I. S.
dc.contributor.other.none.fl_str_mv TORRESBLANCA-BADILLO, ANSELMO
TOWERS, DAVID A.
description The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various varieties of algebras, such as Lie, Leibniz and Malcev algebras. This paper seeks to investigate the extent to which these later theories can be generalised to the variety of all non-associative algebras
publishDate 2020
dc.date.submitted.none.fl_str_mv 2020-11-20
dc.date.issued.none.fl_str_mv 2021-02-17
dc.date.accessioned.none.fl_str_mv 2022-11-15T20:49:49Z
dc.date.available.none.fl_str_mv 2022-11-15T20:49:49Z
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dc.type.spa.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12834/891
dc.identifier.doi.none.fl_str_mv 10.1080/00927872.2021.1877296
dc.identifier.instname.spa.fl_str_mv Universidad del Atlántico
dc.identifier.reponame.spa.fl_str_mv Repositorio Universidad del Atlántico
url https://hdl.handle.net/20.500.12834/891
identifier_str_mv 10.1080/00927872.2021.1877296
Universidad del Atlántico
Repositorio Universidad del Atlántico
dc.language.iso.spa.fl_str_mv eng
language eng
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dc.publisher.place.spa.fl_str_mv Barranquilla
dc.publisher.sede.spa.fl_str_mv Sede Norte
institution Universidad del Atlántico
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https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/891/2/license.txt
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spelling GUTIERREZ, I. S.1ad79c30-8dca-4dd9-b158-8dde1f92aa73TORRESBLANCA-BADILLO, ANSELMOTOWERS, DAVID A.2022-11-15T20:49:49Z2022-11-15T20:49:49Z2021-02-172020-11-20https://hdl.handle.net/20.500.12834/89110.1080/00927872.2021.1877296Universidad del AtlánticoRepositorio Universidad del AtlánticoThe calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various varieties of algebras, such as Lie, Leibniz and Malcev algebras. This paper seeks to investigate the extent to which these later theories can be generalised to the variety of all non-associative algebrasapplication/pdfengCLASSES OF ALGEBRAS AND CLOSURE OPERATIONSPúblico generalinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1BarranquillaSede Norteinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf21. A. Ballester-Bolinches and L. M. Ezquerro. Classes of finite groups. Springer, 2006.2. D. W. Barnes. On the theory of soluble Lie algebras, Math. Zeit. 106 (1968), 343-3543. D.W. Barnes. Saturated formations of soluble Lie algebras in characteristic zero, Archiv. der Math. 30 (1978), 477-480.4. D. W. Barnes. On locally defined formations of soluble Lie and Leibniz Algebras, Bull. Aust. Math. Soc. 86 (2012), 322326 doi:10.1017/S00049727110034435. D. W. Barnes. Schunck Classes of Soluble Leibniz Algebras, Communications in Algebra, 41:11, (2013) 4046-4065, DOI: 10.1080/00927872.2012.7009786. K. Doerk and T. Hawkes. Finite soluble groups. W de Gruyter, 19907. I. S. Gutierrez, and M. Navarro. Clases de ´algebras de Lie y sub´algebras de Cartan. Revista Colombiana de Matem´aticas, vol 42, 2008.8. P. Hall. On the finiteness of certain soluble groups, Proc. London Math. Soc.9(3) (1959). 5956229. P. Hall. On non-strictly simple groups, Proc. Cambridge Philos.Soc.59 (1963). 531553.10. E. I. Marshall. The Frattini subalgebra of a Lie algebra. J. London Math. Soc. 42 (1967), 416-22.11. L. A. Shemetkov, On the product of formations of algebraic systems. Algeb. Logika, 23, No. 6 (1984), 721-72912. L.A. Shemetkov and A. N. Skiba. Formations of AIgebraic Systems [in Russian], Nauka, Moscow (1989).13. A.N. Skiba. Algebra of Formations [in Russian], Belarus. Navuka, Minsk (1997).14. E. L. Stitzinger. On saturated formations of solvable Lie algebras, Pacific J. Math. 47 no. 2 (1973), 531-538.15. E. L. Stitzinger. Supersolvable Malcev algebras, J. Algebra 103 (1986), 69-7916. D. A. Towers. A Frattini theory for algebras. Proc. London Math. Soc. , 27 : 3 (1973), 44046217. K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative, Academic Press, 1982.http://purl.org/coar/resource_type/c_6501ORIGINALClasses_of_Algebras_Final_version_2_.pdfClasses_of_Algebras_Final_version_2_.pdfapplication/pdf368309https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/891/1/Classes_of_Algebras_Final_version_2_.pdf3af89b7c6f9477901f632488fba5e27eMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81306https://repositorio.uniatlantico.edu.co/bitstream/20.500.12834/891/2/license.txt67e239713705720ef0b79c50b2ececcaMD5220.500.12834/891oai:repositorio.uniatlantico.edu.co:20.500.12834/8912022-11-15 15:49:50.88DSpace de la Universidad de Atlánticosysadmin@mail.uniatlantico.edu.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