Completely Prime Modules for Graded Simple Modules Which is Simple Over Leavitt Path Algebra
DOI:
https://doi.org/10.31958/js.v15i1.9202Keywords:
Completely prime module, Graded simple module, Leavitt path Algebra.Abstract
We characterize a graded simple module  in the setting Leavitt path algebras L which is the completely prime module. Let m  M  and r  A, an A-module M is called a completely prime module if    for one m  M  and r  A then 0  or m = 0. In this article, we show that If u is a sink or an infinite emitter, then a graded simple module which is simple  is not a completely prime module.
References
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Abrams, G., Mantese, F., & Tonolo, A. (2015). Extensions of simple modules over Leavitt path algebras. Journal of Algebra, 431. https://doi.org/10.1016/j.jalgebra.2015.01.034
Abrams, G., Rangaswamy, K. M., & Molina, M. S. (2011). The socle series of a Leavitt path algebra. Israel Journal of Mathematics. https://doi.org/10.1007/s11856-011-0074-9
Ara, P., & Pardo, E. (2017). Representing finitely generated refinement monoids as graph monoids. Journal of Algebra, 480. https://doi.org/10.1016/j.jalgebra.2017.02.007
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Arnone, G., & Cortiñas, G. (2022). Graded K-theory and Leavitt path algebras. Journal of Algebraic Combinatorics. https://doi.org/10.1007/s10801-022-01184-5
Chen, X. W. (2015). Irreducible representations of Leavitt path algebras. Forum Mathematicum. https://doi.org/10.1515/forum-2012-0020
Clark, L. O., Barquero, D. M., Gonzalez, C. M., & ... (2016). Using the Steinberg algebra model to determine the center of any Leavitt path algebra. ArXiv Preprint ArXiv …. https://arxiv.org/abs/1604.01079
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Hazrat, R. (2013). The graded structure of Leavitt path algebras. Israel Journal of Mathematics. https://doi.org/10.1007/s11856-012-0138-5
Irawati. (2011). The Generalization of HNP Ring and Finitely Generated Module over HNP Ring. International Journal of Algebra, 5(13).
Pino, G. A., Barquero, D. M., González, C. M., & ... (2010). Socle theory for Leavitt path algebras of arbitrary graphs. Revista Matemática …. https://ems.press/journals/rmi/articles/4627
Rangaswamy, K. M. (2015). On simple modules over Leavitt path algebras. Journal of Algebra, 423. https://doi.org/10.1016/j.jalgebra.2014.10.008
Rangaswamy, K. M. (2020). A survey of some of the recent developments in leavitt path algebras. Leavitt Path Algebras and Classical K-Theory. https://doi.org/10.1007/978-981-15-1611-5_1
Risnawita, Irawati, & Muchtadi-Alamsyah, I. (2021). PRIMENESS OF SIMPLE MODULES OVER PATH ALGEBRAS AND LEAVITT PATH ALGEBRAS. Khayyam Journal of Mathematics, 7(2). https://doi.org/10.22034/kjm.2021.203331.1578
Saleh, K., Astuti, P., & Muchtadi-Alamsyah, I. (2016). On the structure of finitely generated primary modules. JP Journal of Algebra, Number Theory and Applications, 38(5). https://doi.org/10.17654/NT038050519
Wardhana, I. G. A. W., Astuti, P., & Muchtadi-Alamsyah, I. (2016). On almost prime submodules of a module over a principal ideal domain. JP Journal of Algebra, Number Theory and Applications, 38(2). https://doi.org/10.17654/NT038020121
Wardhana, I. G. A. W., Nghiem, N. D. H., Switrayni, N. W., & Aini, Q. (2021). A note on almost prime submodule of CSM module over principal ideal domain. Journal of Physics: Conference Series, 2106(1). https://doi.org/10.1088/1742-6596/2106/1/012011
Abrams, G., Mantese, F., & Tonolo, A. (2015). Extensions of simple modules over Leavitt path algebras. Journal of Algebra, 431. https://doi.org/10.1016/j.jalgebra.2015.01.034
Abrams, G., Rangaswamy, K. M., & Molina, M. S. (2011). The socle series of a Leavitt path algebra. Israel Journal of Mathematics. https://doi.org/10.1007/s11856-011-0074-9
Ara, P., & Pardo, E. (2017). Representing finitely generated refinement monoids as graph monoids. Journal of Algebra, 480. https://doi.org/10.1016/j.jalgebra.2017.02.007
Ara, P., & Rangaswamy, K. M. (2014). Finitely presented simple modules over Leavitt path algebras. Journal of Algebra, 417. https://doi.org/10.1016/j.jalgebra.2014.06.032
Arnone, G., & Cortiñas, G. (2022). Graded K-theory and Leavitt path algebras. Journal of Algebraic Combinatorics. https://doi.org/10.1007/s10801-022-01184-5
Chen, X. W. (2015). Irreducible representations of Leavitt path algebras. Forum Mathematicum. https://doi.org/10.1515/forum-2012-0020
Clark, L. O., Barquero, D. M., Gonzalez, C. M., & ... (2016). Using the Steinberg algebra model to determine the center of any Leavitt path algebra. ArXiv Preprint ArXiv …. https://arxiv.org/abs/1604.01079
Hay, D., Loving, M., Montgomery, M., Ruiz, E., & Todd, K. (2014). Non-stable -theory for Leavitt path algebras. projecteuclid.org. https://doi.org/10.1216/RMJ-2014-44-6-1817.short
Hazrat, R. (2013). The graded structure of Leavitt path algebras. Israel Journal of Mathematics. https://doi.org/10.1007/s11856-012-0138-5
Irawati. (2011). The Generalization of HNP Ring and Finitely Generated Module over HNP Ring. International Journal of Algebra, 5(13).
Pino, G. A., Barquero, D. M., González, C. M., & ... (2010). Socle theory for Leavitt path algebras of arbitrary graphs. Revista Matemática …. https://ems.press/journals/rmi/articles/4627
Rangaswamy, K. M. (2015). On simple modules over Leavitt path algebras. Journal of Algebra, 423. https://doi.org/10.1016/j.jalgebra.2014.10.008
Rangaswamy, K. M. (2020). A survey of some of the recent developments in leavitt path algebras. Leavitt Path Algebras and Classical K-Theory. https://doi.org/10.1007/978-981-15-1611-5_1
Risnawita, Irawati, & Muchtadi-Alamsyah, I. (2021). PRIMENESS OF SIMPLE MODULES OVER PATH ALGEBRAS AND LEAVITT PATH ALGEBRAS. Khayyam Journal of Mathematics, 7(2). https://doi.org/10.22034/kjm.2021.203331.1578
Saleh, K., Astuti, P., & Muchtadi-Alamsyah, I. (2016). On the structure of finitely generated primary modules. JP Journal of Algebra, Number Theory and Applications, 38(5). https://doi.org/10.17654/NT038050519
Wardhana, I. G. A. W., Astuti, P., & Muchtadi-Alamsyah, I. (2016). On almost prime submodules of a module over a principal ideal domain. JP Journal of Algebra, Number Theory and Applications, 38(2). https://doi.org/10.17654/NT038020121
Wardhana, I. G. A. W., Nghiem, N. D. H., Switrayni, N. W., & Aini, Q. (2021). A note on almost prime submodule of CSM module over principal ideal domain. Journal of Physics: Conference Series, 2106(1). https://doi.org/10.1088/1742-6596/2106/1/012011
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2023-06-14
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