# Prof. Dinesh Khurana

### (Past Assistant Professor)

**Research Area:**Non Commutative Algebra

**Brief bio:**

Professor Dinesh Khurana had been an Assistant Professor in the Department of Mathematical Sciences at IISER Mohali during the period 2008–2011. Moving to Panjab University, he had been an Assistant Professor during 2011-2012, an Associate Professor during 2012–2015, and a Professor since 2015.

Professor Khurana has been a fellow of the National Academy of Sciences since 2018. He has been on the editorial board of the Indian Journal of Pure and Applied Mathematics since 2020, and Associate Editor of Beitrage zur Algebra und Geometrie since 2020. His research interests are in Associative rings and algebras, Group theory, Linear and multilinear algebra and matrix theory. His is an author of over 40 research papers and some of his selected works are as follows:

(1) Dinesh Khurana, Lifting potent elements modulo nil ideals. J. Pure Appl. Algebra 225 (2021), no. 11, Paper No. 106762, 7 pp.

(2) Dinesh Khurana, T. Y. Lam and Pace P. Nielsen, An ensemble of idempotent lifting hypotheses. J. Pure Appl. Algebra 222 (2018), no. 6, 1489–1511.

(3) Dinesh Khurana, T. Y. Lam and Pace P. Nielsen, Exchange elements in rings, and the equation XA−BX=I. Trans. Amer. Math. Soc. 369 (2017), no. 1, 495–516.

(4) Dinesh Khurana, Unit-regularity of regular nilpotent elements. Algebr. Represent. Theory 19 (2016), no. 3, 641–644.

(5) Dinesh Khurana, T. Y. Lam and Pace P. Nielsen, Two-sided properties of elements in exchange rings. Algebr. Represent. Theory 18 (2015), no. 4, 931–940.

(6) Shelly Garg, Harpreet K. Grover and Dinesh Khurana, Perspective rings. J. Algebra 415 (2014), 1–12.

(7) Alexander Diesl, Thomas Dorsey, Shelly Garg and Dinesh Khurana, A note on completeness and strongly clean rings. J. Pure Appl. Algebra 218 (2014), no. 4, 661–665.

(8) Zhou Wang, Jianlong Chen, Dinesh Khurana and T. Y. Lam, Rings of idempotent stable range one. Algebr. Represent. Theory 15 (2012), no. 1, 195–200.

(9) Dinesh Khurana, T. Y. Lam and Zhou Wang, Rings of square stable range one. J. Algebra 338 (2011), 122–143.

(10) R. N. Gupta, Anjana Khurana, Dinesh Khurana and T. Y. Lam, Rings over which the transpose of every invertible matrix is invertible. J. Algebra 322 (2009), no. 5, 1627–1636.

(11) V. P. Camillo, D. Khurana, T. Y. Lam, W. K. Nicholson and Y. Zhou, Continuous modules are clean. J. Algebra 304 (2006), no. 1, 94–111.

(12) Dinesh Khurana and T. Y. Lam, Rings with internal cancellation. J. Algebra 284 (2005), no. 1, 203–235.

(13) Dinesh Khurana and T. Y. Lam, Clean matrices and unit-regular matrices. J. Algebra 280 (2004), no. 2, 683–698.