Subject Area: Valuation Theory; Applications of valuations to algebraic number fields; Irreducibility of polynomials over valued fields

I am mainly interested in valuations, specially in their applications to algebraic number theory and other basic problems of algebra like discovering criteria for irreducibility of polynomials. I along with my collaborators have used prolongations of valuations to simple transcendental extensions to generalize the classical Eisenstein-Dumas Irreducibility Criterion, Sch�nemann Irreducibility Criterion, Hensels Lemma, Ehrenfeuchts Irreducibility Criterion and Akira Criterion. I jointly with my research student worked on the irreducibility of truncated binomial expansions over rationals using Newton polygons with respect to p-adic valuations.I also worked on the invariants associated with irreducible polynomials with coefficients in henselian valued fields using saturated distinguished chains. Currently I am exploring the possibility of applying these invariants to some other problems in algebra.

- (with S. Kumar), On irreducible factors of polynomials over complete fields, Journal of Algebra and its Applications 12 (2013).
- (with S. Kumar), On prolongations of valuations via Newton polygons and liftings of polynomials, Journal of pure and Applied Algebra 216 (2012), 2648-2656.
- (with A. Bishnoi), On algebraically maximal valued fields and defectless extensions, Canad. Math. Bull. 55 (2012), 233–241.
- (with A. P. Singh), On a theorem of Tignol for defectless extensions and its converse, Journal of Algebra 288 (2005), 400–408.
- (with J. Saha), A uniqueness problem in valued function fields of conics, Bull. London Math. Soc. 28 (1996), 455–460.
- (with I. S. Luthar), The Brauer-Siegel theorem for algebraic function fields, J. Reine Angew. Math. 299/300 (1978), 108–111.