Geodesic
k-Simplicity of Leavitt Path Algebras with Coefficients in a k-Semifield
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 241-253.

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In this paper, we consider Leavitt path algebras having coefficients in a k-semifield. Concentrating on the aspect of k-simplicity, we find a set of necessary and sufficient conditions for the k-simplicity of the Leavitt path algebra LS(Γ) of a directed graph Γ over a non-zeroid k-semifield S.
Keywords: Leavitt path algebra, semiring, semifield, k-semifield, k-simplicity 
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Gupta, Raibatak Sen; Sen, M.K. k-Simplicity of Leavitt Path Algebras with Coefficients in a k-Semifield. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 241-253. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a0/

[1] G. Abrams and G. Aranda Pino, The Leavitt path algebra of a graph, J. Algebra 293 (2005) 319–334. https://doi.org/10.1016/j.jalgebra.2005.07.028

[2] G. Abrams and G. Aranda Pino, The Leavitt path algebras of arbitrary graphs, Houston J. Math. 34 (2008) 423–442. http://agt.cie.uma.es/~gonzalo/papers/AA3_Web.pdf

[3] G. Abrams, Leavitt path algebras: the first decade, Bull. Math. Sci. 5 (2015) 59–120. https://doi.org/10.1007/s13373-014-0061-7

[4] M.R. Adhikari, M.K. Sen and H.J. Weinert, On k-regular semirings, Bull. Cal. Math. Soc. 88 (1996) 141–144.

[5] J. Cuntz, Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977) 173–185. https://doi.org/10.1007/BF01625776

[6] J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980) 251–268. https://doi.org/10.1007/BF01390048

[7] J.S. Golan, Semirings and their Applications (Kluwer Academic Publishers, 1999).

[8] U. Hebisch and H.J. Weinert, Semirings: Algebraic Theory and Applications in Computer Science (World Scientific, Singapore, 1998).

[9] Y. Katsov, T.G. Nam and J. Zumbrägel, Simpleness of Leavitt path algebras with coefficients in a commutative semiring, Semigroup Forum 94 (2016) 481–499. https://doi.org/10.1007/s00233-016-9781-1

[10] W.G. Leavitt, The module type of a ring, Trans. Amer. Math. Soc. 42 (1962) 113–130. https://doi.org/10.1090/S0002-9947-1962-0132764-X

[11] M.K. Sen and M.R. Adhikari, On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118 (1993) 699–703. https://doi.org/10.1090/S0002-9939-1993-1132423-6

[12] M.K. Sen and A.K. Bhuniya, On additive idempotent k-regular semirings, Bull. Cal. Math. Soc. 93 (2001) 371–384.

[13] R. Sen Gupta, S.K. Maity and M.K. Sen, Leavitt path algebras with coefficients in a Clifford semifield, Comm. Algebra 47 (2019) 660–675. https://doi.org/10.1080/00927872.2018.1492589

[14] M. Tomforde, Leavitt path algebras with coefficients in a commutative ring, J. Pure Appl. Alg. 215 (2011) 471–484. https://doi.org/10.1016/j.jpaa.2010.04.031