Kesemiprimaan Aljabar Lintasan dan Aljabar Lintasan Leavit
DOI:
https://doi.org/10.14421/fourier.2017.61.9-20Keywords:
semigrupring, prima mendasar, semiprima mendasarAbstract
Aljabar lintasan RE dan aljabar lintasan Leavitt LR (E) atas ring komutatif unital R dikonstruksi dari semigrupring yang merupakan aljabar asosiatif dan bebas. Syarat perlu dan cukup RE prima mendasar, semiprima mendasar dan LR (E) prima mendasar masing-masing berkaitan dengan struktur grafnya. Akan tetapi, kesemiprimaan LR (E) bergantung pada R yang semiprima. Hal ini berakibat sebarang aljabar lintasan leavitt atas lapangan selalu semiprima.
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References
[1] Abrams, G. and Aranda Pino, G., 2008, The Leavitt Path Algebra of Arbitrary Graph, Houston J. Math., 34, pp. 423 - 442.
[2] Abrams, G., Aranda Pino, G., and Molina, M.S., 2008, Locally Finite Leavitt Path Algebra, Israel J. Math., 165, pp. 329 - 348.
[3] Abrams, G., Ara, P. and Molina M.S., 2014, Leavitt Path Algebras, A Primer and Handbook, Springer, To appear. https://www.dropbox.com/s/ gqqx735jddrip8f/ AbramsAraSiles_BookC1C2.pdf/dl=0
[4] Aranda Pino, G., Perera, F., Molina, M. S., 2007, Graph algebras: bridging the gap between analysis and algebra, University of Malaga Press, Spain.
[5] Aranda Pino, G., Pardo, E., Molina, M.S., 2009, Prime Spectrum and Primitive Leavitt Path Algebras, Indiana Univ. Math. Journal 58, 869 – 890.
[6] Aranda Pino, G. , Barquero, D. M., Gonzalev, C. M., Molina, M. S., 2010, Socle Theory for Leavitt Path Algebra of Arbitrary Graph, Rev. Mat Iber. 26, pp. 611 – 638.
[7] Assem, I., Simson, D., Skowronski, A., 2005, Elements of the Representation Theory of Associative Algebras, Cambridge University Press, New York.
[8] Passman, D., 1997, The Algebraic Structure of Group Rings, John Wiley and Sons, New York.
[9] Tomforde, M., 2011, Leavitt Path Algebras With Coefficient In A Commutative Ring, J. Pure Appl. Algebra 215, pp. 471-484.
[10] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2011, The Cuntz-Krieger Uniqueness Theorem of Leavitt Path Algebras, Proceedings of â€The 6th SEAMS-UGM Conference 2011†Algebra, pp. 183 – 192.
[11] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2014, Keprimaan Mendasar Aljabar Lintasan Leavitt Atas Ring Komutatif, Artikel dipresentasikan dalam Seminar Nasional Aljabar dan Pengajarannya, di Jurusan Matematika Universitas Hasanudin Makassar, 3 – 4 Mei, 2014.
[12] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2014, On Primeness of Path Algebras over a Commutative Unital Ring, JP Journal of Algebra, Number Theory and Applications, 34 (2), pp. 121 – 138.
[13] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2015, On Free Ideal in Free Algebra over a Ring, J. Indones. Math. Soc., 21 (1), pp. 59 – 69.
[2] Abrams, G., Aranda Pino, G., and Molina, M.S., 2008, Locally Finite Leavitt Path Algebra, Israel J. Math., 165, pp. 329 - 348.
[3] Abrams, G., Ara, P. and Molina M.S., 2014, Leavitt Path Algebras, A Primer and Handbook, Springer, To appear. https://www.dropbox.com/s/ gqqx735jddrip8f/ AbramsAraSiles_BookC1C2.pdf/dl=0
[4] Aranda Pino, G., Perera, F., Molina, M. S., 2007, Graph algebras: bridging the gap between analysis and algebra, University of Malaga Press, Spain.
[5] Aranda Pino, G., Pardo, E., Molina, M.S., 2009, Prime Spectrum and Primitive Leavitt Path Algebras, Indiana Univ. Math. Journal 58, 869 – 890.
[6] Aranda Pino, G. , Barquero, D. M., Gonzalev, C. M., Molina, M. S., 2010, Socle Theory for Leavitt Path Algebra of Arbitrary Graph, Rev. Mat Iber. 26, pp. 611 – 638.
[7] Assem, I., Simson, D., Skowronski, A., 2005, Elements of the Representation Theory of Associative Algebras, Cambridge University Press, New York.
[8] Passman, D., 1997, The Algebraic Structure of Group Rings, John Wiley and Sons, New York.
[9] Tomforde, M., 2011, Leavitt Path Algebras With Coefficient In A Commutative Ring, J. Pure Appl. Algebra 215, pp. 471-484.
[10] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2011, The Cuntz-Krieger Uniqueness Theorem of Leavitt Path Algebras, Proceedings of â€The 6th SEAMS-UGM Conference 2011†Algebra, pp. 183 – 192.
[11] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2014, Keprimaan Mendasar Aljabar Lintasan Leavitt Atas Ring Komutatif, Artikel dipresentasikan dalam Seminar Nasional Aljabar dan Pengajarannya, di Jurusan Matematika Universitas Hasanudin Makassar, 3 – 4 Mei, 2014.
[12] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2014, On Primeness of Path Algebras over a Commutative Unital Ring, JP Journal of Algebra, Number Theory and Applications, 34 (2), pp. 121 – 138.
[13] Wardati, K., Wijayanti, I.E., Wahyuni, S., 2015, On Free Ideal in Free Algebra over a Ring, J. Indones. Math. Soc., 21 (1), pp. 59 – 69.
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Published
2017-04-03
How to Cite
Wardati, K. (2017). Kesemiprimaan Aljabar Lintasan dan Aljabar Lintasan Leavit. Jurnal Fourier, 6(1), 9–20. https://doi.org/10.14421/fourier.2017.61.9-20
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