ON LOCALLY UNIT REGULARITY CONDITIONS FOR ARBITRARY LEAVITT PATH ALGEBRAS

Year 2018, Volume: 67 Issue: 2, 11 - 18, 01.08.2018

Tufan Özdın

Keywords

Leavitt path algebra, von Neumann regular ring, locally regular ring, endomorphism ring

References

• Abrams, G. and Aranda Pino, G., The Leavitt path algebra of a graph, J. Algebra, (2005), (2) , 319-334.
• Abrams, G., Aranda Pino, G., Perera, F. and Siles Molina, M., Chain conditions for Leavitt path algebras, Forum Mathematicum, (2010), 22 (1), 95-114.
• Abrams, G. and Rangaswamy, K. M., Regularity conditions for arbitrary Leavitt path alge- bras, Algebras and Representation Theory, (2010), 13 (3), 319-334.
• Ara, P., Moreno, M. A. and Pardo, E., Nonstable K-theory for graph algebras, Algebras and Representation Theory, (2007), 10, 157-178.
• Aranda Pino, G., Rangaswamy, K. M and Siles Molina, M., Endomorphism rings of Leavitt path algebras, Journal of Pure and Applied Algebra, (2015), 219(12), 5330-5343. Cuntz, J., Simple C algebras generated by isometries, Commun. Math. Phys., (1977), 57, 185.
• Goodearl, K. R., Von Neumann Regular Rings, Pitman, London, 1979.
• Ehrlich, G., Unit regular rings, Portugal. Math., (1968), 27, 209-212.
• Fuller, K. R., On rings whose left modules are direct sums of …nitely generated modules, Proc. Amer. Math. Soc., (1976), 54, 39-44.
• Henriksen, M., On a class of regular rings that are elementary divisor rings, Archive der Mathematik, (1973), 24, 133-141.
• Leavitt, W., The module type of a ring, Trans. Amer. Math. Soc., (1962), 103, 113-130.
• Lee, G., Tariq, R. S. and Cosmin, S. R., Dual Rickart modules, Commun. in Algebra, (2011), , 4036-4058.
• Nicholson, W. K. and Sanchez, C. E., Morphic Modules, Commun. in Algebra, (2005), 33, 2647.
• Özdin T., On endomorphism rings of Leavitt path algebras, Filomat (Submitted). Raeburn, I., Graph algebras, CBMS Regional Conference Series in Mathematics, 103, Pub- lished for the Conference Board of the Mathematical Sciences,(Washington DC, USA, the AMS), 2005.
• Va˜s, L., Canonical traces and direct …nite Leavitt path algebras, Algebras and Representation Theory, (2015), 18(3), 711 âe“ 738.
• Ware, R., Endomorphism rings of projective modules, Trans. Amer. Math. Soc., (1971), (1), 233-256.
• Current address : Tufan ÖZDIN: Department of Mathematics, Faculty of Science and Art, Erzincan University, 24100 Erzincan, TURKEY.
• E-mail address : [e-mail]; [e-mail] ORCID Address: http://orcid.org/0000-0001-8081-1871