The Leavitt path algebras have Hermite property
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Abstract
In this paper, we establish a necessary condition for Leavitt path algebra of a finite graph with coefficients of Hermite ring in a field. Besides, we also provide some examples of this algebra type.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Keywords
Leavitt path algebra, Hermite ring
References
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[4]. G. Abrams and M. Kanuni (2013), “Cohn path algebras have invariant basic number”, arXiv id:1303.2122v2.
[5]. P. Ara, A. Moreno and E. Pardo (2007), “Nonstable K-theory for graph algebras”, Algebra Represent Theory, 2 (10), p. 157-178.
[6]. P. M. Cohn (2000), “From Hermite rings to Sylvester domains”, Proc. Amer. Math. Soc, 7 (128), p. 1899-1904.
[7]. P. M. Cohn (2006), Free ideal rings and localization in general rings, New Mathematical Monographs, 3. Cambridge University Press, Cambridge.
[8]. T. Y. Lam (2006), Serre's problem on projective modules, Springer Monographs in Mathematics. Springer-Verlag, Berlin.
[2]. G. Abrams, P. Ara and M. S. Molina, Leavitt path algebras, Lecture Notes in Mathematics series, Springer-Verlag Inc. (to appear).
[3]. G. Abrams, G. Aranda Pino and M. Siles Molina (2008), “Locally finite Leavitt path algebras”, Israel J. Math, (165), p. 329-348.
[4]. G. Abrams and M. Kanuni (2013), “Cohn path algebras have invariant basic number”, arXiv id:1303.2122v2.
[5]. P. Ara, A. Moreno and E. Pardo (2007), “Nonstable K-theory for graph algebras”, Algebra Represent Theory, 2 (10), p. 157-178.
[6]. P. M. Cohn (2000), “From Hermite rings to Sylvester domains”, Proc. Amer. Math. Soc, 7 (128), p. 1899-1904.
[7]. P. M. Cohn (2006), Free ideal rings and localization in general rings, New Mathematical Monographs, 3. Cambridge University Press, Cambridge.
[8]. T. Y. Lam (2006), Serre's problem on projective modules, Springer Monographs in Mathematics. Springer-Verlag, Berlin.
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