K-álgebras finitas conmutativas con unidad
Main Article Content
Keywords
K-Álgebras de dimensión finita, suma directa, Isomorfismos de álgebras
Resumen
En este artículo presentamos un estudio sobre las K-álgebras finitas, es decir las K-álgebras conmutativas con unidad que son espacios vectoriales de dimensión finita sobre un cuerpo K. Estas son suma directa de K-álgebras finitas locales. Caracterizamos la K-álgebra finita local K[x]/(f(x)), mostramos que ciertas K-álgebras finitas son isomorfas y descomponemos la K-álgebra finita K[x]/(f(x)) en K-álgebras finitas locales.
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Referencias
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[4] R. Vale, Topics in finite-dimensional algebras. Cornell University, 2009. [Online]. Available: http://www.math.cornell.edu/~rvale/fdalgebras.pdf 33,47
[5] M. F. Atiyah and I. G. Macdonald, Introducción al álgebra conmutativa. Barcelona: Editorial Reverté S. A., 1980. 33, 34, 35, 47
[6] N. Bourbaki, Commutative algebra. Paris: Hermann, Publishers in Arts and Science, 1989. 33, 47
[7] D. Eisenbud, Commutative Algebra, with a view toward Algebraic Geometry. New York: Springer-Verlag, 1995. 33, 47
[8] H. Matsumura, Commutative ring theory, 2nd ed. Cambridge: Cambridge University Press, 1989. 33, 47
[9] J. A. Navarro, Algebra conmutativa básica. Badajoz: Universidad de Extremadura, 1997. 33, 47
[10] W. Murray, “Nacayama automorphisms of Frobenius algebras,” Journal of algebra, vol. 269, no. 2, pp. 599–609, 2003. [Online]. Available: http://dx.doi.org/10.1016/S0021-8693(03)00465-4 33, 47
[11] A. J. Lindenhovius, “Classifying finite-dimensional C*-algebras by posets of their commutative C*-Subalgebras,” Int. J. Theor Phys, vol. 54, no. 12, pp. 4615–4635, 2015. [Online]. Available: http://dx.doi.org/10.1007/s10773-015-2817-6 33, 47
[12] C. Heunen and A. J. Lindenhovius, “Domains of commutative C*- Subalgebras,” arXiv:1504.02730v4, p. 25, 2016. [Online]. Available: https://arxiv.org/abs/1504.02730v4 33, 47
[13] C. Heunen, “Characterizations of categories of commutative C*-Subalgebras,” Communications in Mathematical Physics, vol. 331, no. 1, pp. 215–238, 2014. [Online]. Available: http://dx.doi.org/10.1007/s00220-014-2088-8 33, 47
[14] J. Hamhalter, “Isomorphisms of ordered structures of abelian C∗- subalgebras of C∗-algebras,” Journal of Mathematical Analysis and Applications, vol. 383, no. 2, 2011. [Online]. Available: http://dx.doi.org/10.1016/j.jmaa.2011.05.035 33, 47
[15] E. Hartmann, Planar Circle Geometries: an introduction to Moebius-, Laguerre- and Minkowski-planes. Springer-Verlag, 2004. 34, 47
[16] S. Mazuelas, Interpretación proyectiva de las geometrías métricas, equiformes e inversivas. Tesis doctoral . Director: J.M. Aroca, 2008. [Online]. Available: https://www.educacion.gob.es/teseo/mostrarRef.do?ref=676503 34
[17] ——, “Interpretación proyectiva de las métricas del plano real,” Rev. Semin. Iberoam. Mat., vol. 3, no. VI fasc. 3, pp. 109–125, 2008. [Online]. Available: http://ctri.uva.es/ctri/images/stories/documentos/rsim3v-vi.pdf 34
[18] H. Havlicek and K. List, “A three-Dimensional Laguerre geometry and its visualization,” In proceedinhs-Dresden Symposium geometry: constructive and kinematic, vol. Institut f, pp. 122–129, 2013. [Online]. Available: https://arxiv.org/abs/1304.0223 34, 47