King Fahd University of Petroleum & Minerals                                                                       Department of Mathematics and Statistics

Commutative Algebra Research Group (CARG)

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Funded Research Projects by CARG Members


Projects In Progress ___________ _______________________________________________________________________

  1. J. Abuihlail, Homological dimensions for semimodules

  2. J. Abuihlail (PI), O. Echi  (and H. Hroub, PhD candidate), Unifying Zariski-like topologies for modules

  3. S. Kabbaj (PI), A. Mimouni (and A. Kadri, PhD candidate), t-Reductions of ideals in integral domains 

  4. S. Kabbaj, Bi-amalgamated algebras along ideals

  5. A. Mimouni, Factoring ideals and stability in integral domains

  6. A. Mimouni, Transfer of some ring-theoretic properties to trivial extensions, amalgamations, and pullbacks

  7. A. Tatar, Extensions of Picard 2-stacks and torsors

      NSTIP Proposals

  1. J. Abuihlail (PI), A. Laradji (and R. Noegraha, PhD candidate), Wisbauer Categ. for semimod. over semirings

  2. S. Kabbaj (PI), A. Tatar (and K. Adarbeh, PhD candidate), Vanishing of cohomol. over comm.  extensions

Projects Completed ____________________________________________________________________________________

  1. J. Abuihlail, Almost Perfect Rings.

  2. J. Abuihlail, Semibialgebras and Hopf Semialgebras.

  3. J. Abuihlail, On Exact Sequences of Semimodules over Semirings.

  4. J. Abuihlail, Zariski-like Topologies for Modules over Commutative Rings.

  5. J. Abuihlail and M. Jarrar, Tilting Modules over Commutative Rings.

  6. J. Abuihlail, Semicorings and Semicomodules.

  7. J. Abuihlail, Primeness & Coprimeness Conditions for Comodules & Corings.

  8. J. Abuihlail and S. Kabbaj (Consultant), Tilting and Cotilting Modules over Commutative Rings (Junior).

  9. J. Abuihlail, Strongly Hollow Modules.

  10. J. Abuihlail, Monads and Comonads in Varieties.

  11. I. AlRasasi and S. Kabbaj (Consultant), Integer-Valued Polynomials and Bhargava Rings (Junior).

  12. P. Bakhtary, Codimension 2 subvarieties of non-projective varieties

  13. P. Bakhtary (PI) and M. Halic, The Splitting of Vector Bundles on Higher Dimensional Varieties.

  14. O. Echi, A Categorical Study of Typical Examples of Alexandroff Spaces.

  15. O. Echi (PI) and I. AlRasasi, A Generalization of Carmichael Numbers.

  16. M. Halic, Algebraic Hamiltonian/Gauge Theoretical Gromov-Witten invariants.

  17. M. Halic, The GIT fan of affine varieties.

  18. M. Halic, Strong exceptional sequences of vector bundles over a certain class of Fano varieties.

  19. M. Halic, Semi-Stable Vector Bundles over fibred varieties.

  20. M. Halic, Modular Properties of Nodal Curves on K3 Surfaces.

  21. M. Halic (PI) and H. Azad, Holomorphic Sturm-Liouville Systems.

  22. M. Halic, Cohomological Splitting Criteria for Vector Bundles over Surfaces

  23. S. Kabbaj, Trivial Ring Extensions Defined by Gaussian Conditions.

  24. S. Kabbaj, Trivial Ring Extensions Defined by Homological Conditions.

  25. S. Kabbaj, Subalgebras of Affine Domains over Noetherian Domains.

  26. S. Kabbaj (PI) and A. Mimouni, t-Class Semigroups of Integral Domains.

  27. S. Kabbaj, Regularity of Tensor Products of k-Algebras.

  28. S. Kabbaj (PI) and A. Mimouni, Core of Ideals in Integral Domains.

  29. S. Kabbaj, Prüfer Conditions in Amalgamated Duplications

  30. S. Kabbaj, Embedding Dimension of Tensor Products of k-Algebras and Defect of Regularity

  31. A. Mimouni, Compact/Coprime Packedness with Respect to Star Operations.

  32. A. Mimouni, Ratilff-Rush Closure of Ideals in Integral Domains.

  33. A. Mimouni, Some Finiteness Conditions on the set of t-linked overrings.

  34. A. Mimouni and M. S. Samman, Characterization/.. Via Semistar Operations.

  35. A. Mimouni, Transfer of Arithmetical-like Properties to Trivial Extensions.

  36. A. Mimouni, Set Theoretic Complete Intersection Prime Ideals in Poly. Rings over Prüfer Domains and Pullbacks

  37. A. Mimouni, Integral domains in which every ideal is projectively equivalent to a prime ideal

  38. U. Schauz and A. Mimouni (Consultant), Polynomial Method & Berlekamp's Switching Game (Junior).

  39. A. Tatar and S. Kabbaj (Consultant), Extensions of Picard Stacks (Junior).