Sudesh Kaur Khanduja

PIC

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

Background and Research Interests

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.

Select Publications

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