Research

My broad research area is Commutative Algebra. In commutative algebra, we study commutative rings, ideals and modules over commutative rings. The concept of module over a ring is a generalization of the concept of vector space over a field. During my Ph.D, I studied projective modules, unimodular rows and its topological analogue. I am also interested to work in the area of Algebraic Geometry. Currently, I am working on multiplicative Lie algebra, Ore extension of a ring and algebraic analogue of the cohomotopy group.

Publications

• Existence of a unique group of finite order, The Mathematics Student, 81 (1 - 4 ), 215 - 218, 2012 (with Prof. Shiv Datt Kumar).


• On the number of generators of a projective module, Proc. Indian Acad. Sci. (Math. Sci.), 123 (4), 469 - 478, November 2013 (with Prof. Shiv Datt Kumar and Prof. Raja Sridharan).


• On completable unimodular row over a polynomial ring, J. Indian Math. Soc. 82 (1 - 2), 185 - 195, January - June 2015.


• Connection between commutative algebra and topology, Indian J. Pure Appl. Math., 47 (3), 471-489, September 2016 (with Prof. Shiv Datt Kumar and Prof. Raja Sridharan).


• Projective modules and efficient generation of ideals over Laurent polynomial rings, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. , 87(3), 349-353, September 2017 (with Prof. Shiv Datt Kumar and Prof. Raja Sridharan).


• Multiplicative Lie algebras and Schur multiplier, J. Pure Appl. Algebra, 223 (9), 3695-3721, September 2019, (with Prof. Ramji Lal).


• A construction of Bent functions on a finite group, Nat. Acad. Sci. Lett., 43 (3), 247-251, June 2020 (with Mani Shankar Pandey and Dr. Vipul Kakkar).


• The Chapter "On an algebraic analogue of the Mayer-Vietoris sequence", Leavitt Path Algebras and Classical K-Theory, Indian Statistical Institute Series. Springer, 2020, 261-279 (with Prof. Raja Sridharan and Sunil K. Yadav).


• Lie commutator, solvability and nilpotency in multiplicative Lie algebras, J. Algebra Appl., 20 (8), 2150138 (11 pp), 2021 (with Prof. Ramji Lal and Mani Shankar Pandey).


• Theory of extensions of multiplicative Lie algebras, J. Lie Theory, 31 (3), 637-658, September 2021 (with Mani Shankar Pandey).


• Classification of multiplicative Lie algebra structures on a finite group, Colloq. Math., 168, 25-34, 2022 (with Mani Shankar Pandey).


• Simplicity of iterated Ore extensions, Asian-Eur. J. Math., 15 (3), 2250052 (11 pp), 2022 (with Mamta Balodi).


• The algebraic cohomotopy group and its properties, Indian J. Pure Appl. Math., 54, 641-648, 2023 (with Prof. Raja Sridharan and Sunil K. Yadav).


• The Schur multiplier of some finite multiplicative Lie algebras, J. Lie Theory, 34 (2), 423-436, 2024 (with Amit Kumar, Deepak Pal, and Seema Kushwaha).


• A realistic notion of a right gyrogroup action, Proc. Rom. Acad. Ser. A, 25 (1), 27-34, 2024 (with Akshay Kumar and Seema Kushwaha).


• Group completion of a gyrogroup, Nat. Acad. Sci. Lett., in press (with Akshay Kumar, Mani Shankar Pandey, and Seema Kushwaha).


• Nilpotency and capability in multiplicative Lie algebras, Comm. Algebra, in press (with Amit Kumar and Mani Shankar Pandey).


• Some remarks on algebraic fundamental groups, to appear in J. Algebra Appl. (with Prof. Raja Sridharan and Sunil K. Yadav).


• Isoclinism in multiplicative Lie algebras, to appear in Publ. Math. Debrecen (with Mani Shankar Pandey).