A direct proof of Noether's second isomorphism theorem for abelian categories

BARROS, RENATA; POMBO JR., DINAMÉRICO

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.43 no.1 Bogotá Jan./June 2009

A direct proof of Noether's second isomorphism theorem for abelian categories

Prueba directa del segundo teorema de isomorfismo de Noether para categorías abelianas

RENATA BARROS¹, DINAMÉRICO POMBO JR.²

¹Instituto Federal do Rio de Janeiro, Rio de Janeiro, Brasil. Email: reabarros@yahoo.com.br
²Universidade Federal Fluminense, Rio de Janeiro, Brasil. Email: dpombo@terra.com.br

Abstract

A direct and simple proof of Noether's second isomorphism theorem for abelian categories is obtained.

Key words: Abelian categories, Noether isomorphism theorem.

2000 Mathematics Subject Classification: 18E10.

Resumen

Obtenemos una demonstración directa y simple del segundo teorema de isomorfismo de Noether para categorías abelianas.

Palabras clave: Categorías abelianas, teorema del isomorfismo de Noether.

Texto completo disponible en PDF

References

[1] Bucur, I. & Deleanu, A., Introduction to the Theory of Categories and Functors, John Wiley & Sons, New York, 1968. [ Links ]

[2] Freyd, P., Abelian Categories, Harper and Row, New York, 1964. [ Links ]

[3] Grothendieck, A., `Sur quelques points d'algèbre homologique´, Tôhoku Math. J. 9, (1957), 119-221. [ Links ]

[4] Grothendieck, A., Séminaire d'Algèbre Homologique, 1re anée: 1957, Faculté des Sciences de Paris, Paris, 1958. [ Links ]

[5] Hartshorne, R., Algebraic Geometry, Vol. 52 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1977. [ Links ]

[6] Hilton, P. & Wu, Y., A Course in Modern Algebra, John Wiley & Sons, New York, 1974. [ Links ]

[7] Lang, S., Introduction to Differentiable Manifolds, Interscience, New York, 1962. [ Links ]

[8] Mac Lane, S., Categories for the Working Mathematician, Vol. 5 edition Second of Graduate Texts in Mathematics, Springer Verlag, New York, 1998. [ Links ]

(Recibido en mayo de 2008. Aceptado en enero de 2009)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv43n1a04,    

     AUTHOR  = {Barros, Renata and Pombo Jr., Dinamérico},    

     TITLE   = {{A direct proof of Noether's second isomorphism theorem for abelian categories}},    

     JOURNAL = {Revista Colombiana de Matemáticas},    

    YEAR    = {2009},    

    volume  = {43},    

    number  = {1},    

    pages   = {35-42}    

}