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Invertibility of elements in the path algebra of a quiver | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 89-98 اصل مقاله (151.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.27539.1670 | ||
| نویسندگان | ||
| S. Karthika* ؛ M. Viji | ||
| Department of Mathematics, University of Calicut, St. Thomas College, Thrissur, India | ||
| چکیده | ||
| The current study elucidates the nature of right and left inverses of an element in the path algebra of a quiver. A general characterisation of such elements has been established. An explicit formula to calculate the inverse element has been formulated. It is observed that the left and right inverses of an element in the non-commutative path algebraic structure coincides. Furthermore, it is noted that the Jacobson radical of any finite dimensional path algebra can be easily found using this characterisation. | ||
| کلیدواژهها | ||
| Quiver؛ Path algebra؛ Unit element؛ Noncommutative algebra؛ Jacobson radical | ||
| مراجع | ||
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[1] I. Assem, D. Simson and A. Skowronski, Elements of Representation Theory of Associative algebras: Techniques of Representation Theory, London Math. Soc. Stud. Texts., Cambridge Univ. Press, 2001. [2] N. Jacobson, The radical and semi-simplicity for arbitrary rings, Am. J. Math., 67 (1945), 300-320. [3] S. Karthika and M. Viji, Unit elements in the path algebra of an acyclic quiver, Indian J. Pure Appl. Math., 52 (2021), 138-140. [4] E. Spiegel and C. J. O’Donnell, Incidence Algebras, Monographs and Textbooks in Pure Appl. Math., 206 (1997). [5] M. Viji and R. S. Chakravarti, (2012). On quivers and incidence algebra, Glob. J. Sci. Front. Res., 12 (2012). | ||
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