University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 Invertibility of elements in the ‎p‎ath algebra of a quiver 89 98 9317 10.22124/jart.2025.27539.1670 EN S. Karthika Department of‎‎ Mathematics,‎‎ University of Calicut, St‎. ‎Thomas College‎, ‎‎‎Thrissur‎, ‎India M. Viji Department of‎‎ Mathematics,‎‎ University of Calicut, St‎. ‎Thomas College‎, ‎‎‎Thrissur‎, ‎India Journal Article 2024 05 24 ‎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. https://jart.guilan.ac.ir/article_9317_55815b42d12b6f4039ab200d0e9ffd15.pdf