Finite dimensionality of $\operatorname{Ext}^n$'s and $\operatorname{Tor}_n$'s of simple modules over one class of algebras
V. V. Bavula

This publication is cited in the following articles:

1. V.V. Bavula, “Δ-locally nilpotent algebras, their ideal structure and simplicity criteria”, Journal of Pure and Applied Algebra, 2025, 107861  
2. V. V. Bavula, “Inner generalized Weyl algebras and their simplicity criteria”, J. Algebra Appl., 23:13 (2024)  
3. V.V. Bavula, “Description of bi-quadratic algebras on 3 generators with PBW basis”, Journal of Algebra, 631 (2023), 695  
4. Samuel A. Lopes, Farrokh Razavinia, “Quantum generalized Heisenberg algebras and their representations”, Communications in Algebra, 50:2 (2022), 463  
5. V. V. Bavula, V. Levandovskyy, “A Remark on the Dixmier Conjecture”, Can. Math. Bull., 63:1 (2020), 6  
6. V. V. Bavula, “Generalized Weyl algebras and diskew polynomial rings”, J. Algebra Appl., 19:10 (2020), 2050194  
7. V. V. Bavula, “The generalized Weyl Poisson algebras and their Poisson simplicity criterion”, Lett Math Phys, 110:1 (2020), 105  
8. V. Bavula, K. Alnefaie, Contemporary Mathematics, 751, Categorical, Homological and Combinatorial Methods in Algebra, 2020, 33  
9. Ebrahim Ebrahim, “The prime spectrum and representation theory of the 2 × 2 reflection equation algebra”, Communications in Algebra, 47:3 (2019), 1153  
10. V. Bavula, T. Lu, Contemporary Mathematics, 727, Rings, Modules and Codes, 2019, 49  
11. Xiangui Zhao, Qiuhui Mo, Yang Zhang, “Gelfand–Kirillov dimension of generalized Weyl algebras (In memory of Guenter Rudolf Krause (1941–2015))”, Communications in Algebra, 46:10 (2018), 4403  
12. Jonas T. Hartwig, “Noncommutative fiber products and lattice models”, Journal of Algebra, 508 (2018), 35  
13. Munerah Almulhem, Tomasz Brzeziński, “Skew derivations on generalized Weyl algebras”, Journal of Algebra, 493 (2018), 194  
14. V. Bavula, V. Bekkert, V. Futorny, “Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators”, Proc. Amer. Math. Soc., 146:6 (2018), 2373  
15. V. V. Bavula, T. Lu, “Torsion simple modules over the quantum spatial ageing algebra”, Communications in Algebra, 45:10 (2017), 4166  
16. V. V. Bavula, “Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings”, Math.Comput.Sci., 11:3-4 (2017), 253  
17. V. V. Bavula, T. Lu, “The quantum euclidean algebra and its prime spectrum”, Isr. J. Math., 219:2 (2017), 929  
18. V. V. Bavula, T. Lu, “The Prime Spectrum and Simple Modules Over the Quantum Spatial Ageing Algebra”, Algebr Represent Theor, 19:5 (2016), 1109  
19. Commutation Relations, Normal Ordering, and Stirling Numbers, 2015, 419  
20. V. V. Bavula, “Lie algebras of triangular polynomial derivations and an isomorphism criterion for their Lie factor algebras”, Izv. Math., 77:6 (2013), 1067–1104                
21. David A. Jordan, Imogen E. Wells, “Simple ambiskew polynomial rings”, Journal of Algebra, 382 (2013), 46  
22. Hans Erik Nordstrom, “Simple Modules Over Generalized Weyl Algebras and Their Associated Primes”, Communications in Algebra, 40:9 (2012), 3224  
23. V.V. Bavula, “The group of automorphisms of the Jacobian algebra An”, Journal of Pure and Applied Algebra, 216:3 (2012), 535  
24. V. V. BAVULA, “On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra”, Math. Proc. Camb. Phil. Soc., 151:2 (2011), 245  
25. Lionel Richard, Andrea Solotar, “On Morita Equivalence for Simple Generalized Weyl Algebras”, Algebr Represent Theor, 13:5 (2010), 589  
26. Jonas T. Hartwig, “Twisted Generalized Weyl Algebras, Polynomial Cartan Matrices and Serre-Type Relations”, Communications in Algebra, 38:12 (2010), 4375  
27. V.V. Bavula, “The Jacobian algebras”, Journal of Pure and Applied Algebra, 213:5 (2009), 664  
28. V.V. Bavula, “The Carlitz algebras”, Journal of Pure and Applied Algebra, 212:5 (2008), 1175  
29. Paul Levy, “Isomorphism problems of noncommutative deformations of type 𝐷 Kleinian singularities”, Trans. Amer. Math. Soc., 361:5 (2008), 2351  
30. Lars Hellström, Sergei D. Silvestrov, “Ergodipotent maps and commutativity of elements in noncommutative rings and algebras with twisted intertwining”, Journal of Algebra, 314:1 (2007), 17  
31. Jonas T. Hartwig, “Locally finite simple weight modules over twisted generalized Weyl algebras”, Journal of Algebra, 303:1 (2006), 42  
32. Ellen Kirkman, James Kuzmanovich, “Fixed subrings of Noetherian graded regular rings”, Journal of Algebra, 288:2 (2005), 463  
33. V. Bavula, F. van Oystaeyen, “Simple modules of the Witten–Woronowicz algebra”, Journal of Algebra, 271:2 (2004), 827  
34. V. Bavula, “Solutions to two questions about the Weyl algebras”, Proc. Amer. Math. Soc., 133:6 (2004), 1587  
35. Ellen E. Kirkman, Lance W. Small, “EXAMPLES OF FCR-ALGEBRAS”, Communications in Algebra, 30:7 (2002), 3311  
36. V.V Bavula, T.H Lenagan, “Krull Dimension of Generalized Weyl Algebras with Noncommutative Coefficients”, Journal of Algebra, 235:1 (2001), 315  
37. V. Bavula, D. Jordan, “Isomorphism problems and groups of automorphisms for generalized Weyl algebras”, Trans. Amer. Math. Soc., 353:2 (2000), 769  
38. V. Bavula, “The simple modules of the ore extensions with coefficients from a dedekind ring”, Communications in Algebra, 27:6 (1999), 2665  
39. V Bavula, F van Oystaeyen, “Krull Dimension of Generalized Weyl Algebras and Iterated Skew Polynomial Rings: Commutative Coefficients”, Journal of Algebra, 208:1 (1998), 1  
40. V Bavula, F van Oystaeyen, “The Simple Modules of Certain Generalized Crossed Products”, Journal of Algebra, 194:2 (1997), 521  
41. Vladimir Bavula, “Filter dimension of algebras and modules, a simplicity criterion of generalized weyl algebras”, Communications in Algebra, 24:6 (1996), 1971  
42. V. V. Bavula, “Indentification of the Hilbert function and Poincaré series, and the dimension of modules over filtered rings”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 225–246