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Elad Paran, Professor

Elad Paran
Contact Info

The Open University of Israel 1 University Road, P. O. Box 808, Raanana 4353701
Office:972-9-7781856 Fax:972-9-7780856 Email:paran@openu.ac.il
Born:1982

Additional Information

My CRIS profile

Areas of Interest
  • Ring theory, noncommutative algebra, geometry over division rings, arithmetic of skew polynomial rings, algebraic combinatorics, Field Arithmetic and Galois theory, arithmetic of rings of formal power series

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2005 - 2009
Ph.D., Mathematics, With Distinction, Tel Aviv University
2003 - 2005
M.Sc., Mathematics, Summa Cum Laude, Tel Aviv University
2001 - 2003
B.A.,Computer Science, Magna Cum Laude, Open University of Israel
1998 - 2001
B.A., Mathematics, Magna Cum Laude, Open University of Israel

1. Algebraic patching over complete domains, Israel Journal of Mathematics, 2008, available here.

2. Split embedding problems over complete domains, Annals of Mathematics, 2009, available here.

3. Split embedding problems over function fields over complete domains, American Journal of Mathematics, 2009, available here.

4. Power series over generalized Krull domains, with M. Temkin, Journal of Algebra, 2009, available here.

5. Galois theory over complete domains, Mathematische Annalen, 2010, available here.

6. Fully Hilbertian Fields, with L. Bary-Soroker, Israel Journal of Mathematics, 2009, available here.

7. Patching and admissibility over two-dimensional complete local domains, with D. Neftin, Algebra and Number Theory, 2010, available here.

8. On totally ramified extensions of discrete valued fields, with L. Bary-Soroker, Proceedings of a GTEM conference on Geometry and Arithmetic around Galois Theory, 2010, available here.

9. Hilbertianity of fields of power series, Journal of the Institute of Mathematics of Jussiue, 2012, available here.

10. Galois theory over rings of arithmetic power series, with A. Fehm, Advances in Mathematics, 2011, available here.

11. Non-ample complete valued fields, with A. Fehm, International Mathematics Research Notices, 2011, available here.

12. Galois Theory over Integral Tate Algebras, with M. Jarden, New York Journal of Mathematics, 2012, available here.

13. Klein approximation and Hilbertian fields, with A. Fehm, Journal für die reine und angewandte Mathematik, 2013, available here.

14. Split Embedding Problems over the open arithmetic disc, with A. Fehm, Transactions of the American Mathematical Society, 2014, available here.

15. Algebraic functions in the Wiener algebra, with A. Fehm and N. Lev, Communications in Algebra, 2014, available here.

16. Automorphism groups over Hilbertian fields, with F. Legrand, Journal of Algebra, 2017, available here.

17. Embedding problems for automorphism groups of fields extensions, with A. Fehm and F. Legrand, Bulletin of the London Mathematical Society, 2019, available here.

18. Twin-prime and Goldbach theorems for Z[[x]], Journal of Number Theory, 2020, available here.

19. Galois groups over rational function fields over skew fields, with G. Alon and F. Legrand, Comptes Rendus Mathématique, 2020, available here.

20. The Inverse Galois Problem over C(z), with D. Haran and A. Fehm, Abelian varieties and number theory, Contemp. Math., Amer. Math. Soc., 2021, available here.

21. A quaternionic Nullstellensatz, with G. Alon, Journal of pure and applied algebra, 2021, available here.

22. Completely prime one-sided ideals in skew polynomial rings, with G. Alon, Glasgow Mathematical Journal, 2021, available here.

23. A central quaternionic Nullstellensatz, with G. Alon, Journal of Algebra, 2021, available here.

24. Fixed points and orbits in skew polynomial rings, with A. Chapman, Journal of algebra and its applications, 2023, available here.

25. Combinatorial Nullstellensatz over division rings, Journal of Algebraic Combinatorics, 2023, available here.

26. Luroth's and Igusa's theorems over division rings, with F. Legrand, Osaka Journal of Mathematics, 2023, available here.

27. Generic freeness of modules over non-commutative domains, with V. Thieu, Journal of Algebra, 2024, available here.

28. The Collatz problem in F_p[x] and F_p[[x]], with A. Behajaina, Finite Fields and their applications, 2023, available here.

29. A skew Newton-Puiseux theorem, with V. Thieu, Israel Journal of Mathematics, 2025, Arxiv version available here.

30. The Collatz map in polynomial rings and in completions, with A. Behajaina, Discrete Mathematics, 2025, Arxiv version available here.

31. On the stopping time of the Collatz map in F_2[x], with G. Alon and A. Behajaina, Finite fields and their applications, 2025, Arxiv version available here.

32. On the geometry of zero sets of central quaternionic polynomials, with G. Alon, Journal of Algebra 2025, Arxiv version available here.

33. Noether's normalization in skew polynomial rings, with V. Thieu, Journal of Pure and Applied Algebra, 2025, Arxiv version available here.

34. On the geometry of zero sets of central quaternionic polynomials II, with G. Alon and A. Chapman, to appear in Israel Journal of Mathematics, 2025, Arxiv version available here.

35. On a problem of Amitsur and Small, preprint, Arxiv version available here.

35'. Amitsur Small rings, Journal of Algebra, 2025, available here. (An extended version of the preceding entry, joint with A. Chapman.)

36. Images of polynomial maps and the Ax-Grothendieck theorem over algebraically closed division rings, with T.N. Son, to appear in Journal of pure and applied algebra, 2026, preprint available here.

37. The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and Weak Finitesatz in skew polynomial rings, with G. Alon and A. Behajaina, 2025, preprint available here.

38. Characterization of the centrally finite Amitsur-Small division rings, preprint, 2026.

39. On Landweber's unique factorization problem, with A. Jones, submitted, 2026, preprint available here.

* A survey talk on the main results of [23],[32],[33], [35] is available online here.

M.Sc. Thesis, Tel-Aviv University, 2005, titled Algebraic patching over complete domains, under the guidance of Dan Haran.

Ph.D. Thesis, Tel-Aviv University, 2009, titled Split embedding problems over complete domains, under the guidance of Dan Haran

2010
Rothschild Fellowship.
2010
Fulbright Scholarship
2010
Israel Mathematical Union Nessyahu prize for an outstanding Ph.D. thesis.
2009
TAU faculty of exact sciences Dean’s scholarship
2008
Damm Fellowship
2007
A prize for outstanding Ph.D. studies achievements, Tel Aviv University

- Young students advisor,  2011-2014.

- Member of the committee for accreditation of prior studies, 2012-2014.

- Student seminar supervisor, 2011-2017, 2018-present.  

- Head of the Mathematics unit, 2016-2018.

- Member of the mathematics and computer science senate subcommittee, 2011-present.

- Member of the natural sciences senate subcommittee, 2019-2021, 2023-2027.

- Member of the Open University senate, 2022-present.

- Member of the academic committee of graduate studies authority, 2023-2026.

- Member of the research authority steering committee, 2023-present.

- Associate Editor, Communications in Algebra, 2026-present.