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@article{ADM_2021_32_1_a5, author = {A. Reyes and H. Su\'arez}, title = {Skew {PBW} extensions over symmetric rings}, journal = {Algebra and discrete mathematics}, pages = {76--102}, publisher = {mathdoc}, volume = {32}, number = {1}, year = {2021}, language = {en}, url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a5/} }
A. Reyes; H. Suárez. Skew PBW extensions over symmetric rings. Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 76-102. http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a5/
[1] J. P. Acosta, O. Lezama, “Universal property of skew PBW extensions”, Algebra Discrete Math., 20:1 (2015), 1–12 | MR | Zbl
[2] D. D. Anderson, V. Camillo, “Armendariz rings and Gaussian rings”, Comm. Algebra, 26:7 (1998), 2265–2272 | DOI | MR | Zbl
[3] S. Annin, “Associated primes over Ore extension rings”, J. Algebra Appl., 3:2 (2004), 193–205 | DOI | MR | Zbl
[4] V. A. Artamonov, “Derivations of skew PBW extensions”, Commun. Math. Stat., 3:4 (2015), 449–457 | DOI | MR | Zbl
[5] V. A. Artamonov, O. Lezama, W. Fajardo, “Extended modules and Ore extensions”, Commun. Math. Stat., 4:2 (2016), 189–202 | DOI | MR | Zbl
[6] J. Apel, Gröbnerbasen in nichtkommutativen Algebren und ihre Anwendung (Gröbner bases in noncommutative algebras and their applications), Karl-Marx-Univ., Leipzig, 1988 | Zbl
[7] H. E. Bell, “Near-rings in which each element is a power of itself”, Bull. Aust. Math. Soc., 2:3 (1970), 363–368 | DOI | MR | Zbl
[8] A. D. Bell, K. Goodearl, “Uniform rank over differential operator rings and Poincaré-Birkhoff-Witt extensions”, Pacific J. Math., 131:11 (1988), 13–37 | DOI | MR | Zbl
[9] A. D. Bell, S. P. Smith, Some 3-dimensional skew polynomial ring, University of Wisconsin, Milwaukee, preprint, 1990
[10] J. Bueso, J. Gómez-Torrecillas, A. Verschoren, Algorithmic Methods in Non-commutative Algebra. Applications to Quantum Groups, Kluwer, Dordrecht, 2003 | MR | Zbl
[11] W. Fajardo, C. Gallego, O. Lezama, A. Reyes, H. Suárez, H. Venegas, Skew PBW Extensions. Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications, Algebra and Applications, Springer, Cham, 2020 | DOI | MR | Zbl
[12] A. M. Gavrilik, A. U. Klimik, “$q$-Deformed orthogonal and pseudo-orthogonal algebras and their representations”, Lett. Math. Phys., 21:3 (1991), 215–220 | DOI | MR | Zbl
[13] C. Gallego, O. Lezama, “Gröbner bases for ideals of $\sigma$-PBW extensions”, Comm. Algebra, 39:1 (2011), 50–75 | DOI | MR | Zbl
[14] C. Gallego, O. Lezama, “Matrix approach to noncommutative stably free modules and Hermite rings”, Algebra Discrete Math., 18:1 (2014), 109–137 | MR | Zbl
[15] M. Hamidizadeh, E. Hashemi, A. Reyes, “A classification of ring elements in skew PBW extensions over compatible rings”, Int. Electron. J. Algebra, 28 (2020), 75–97 | DOI | MR | Zbl
[16] E. Hashemi, A. Moussavi, H. Haj Seyyed Javadi, “Polynomial Ore extensions of Baer and p.p.-rings”, Bull. Iranian Math. Soc., 29:2 (2003), 65–86 | MR | Zbl
[17] E. Hashemi, K. Khalilnezhad, A. Alhevaz, “$(\Sigma,\Delta)$-Compatible Skew PBW Extension Ring”, Kyungpook Math. J., 57:3 (2017), 401–417 | MR | Zbl
[18] E. Hashemi, K. Khalilnezhad, A. Alhevaz, “Extensions of rings over 2-primal rings”, Matematiche (Catania), 74:1 (2019), 141–162 | MR | Zbl
[19] E. Hashemi, K. Khalilnezhad, M. Ghadiri, “Baer and quasi-Baer properties of skew PBW extensions”, J. Algebr. Syst., 7:1 (2019), 1–24 | MR | Zbl
[20] C. Huh, C. Lee, A. Smoktunowicz, “Armendariz rings and semicommutative rings”, Comm. Algebra, 30:2 (2002), 751–761 | DOI | MR | Zbl
[21] A. P. Isaev, P. N. Pyatov, V. Rittenberg, “Diffusion algebras”, J. Phys. A., 34:29 (2001), 5815–5834 | DOI | MR | Zbl
[22] H. Jiménez, O. Lezama, “Gröbner bases of modules over $\sigma$-PBW extensions”, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 32 (2016), 39–66 | MR
[23] A. Kandri-Rody, V. Weispfenning, “Non-commutative Gröbner Bases in Algebras of Solvable Type”, J. Symbolic Computation, 9:1 (1990), 1–26 | DOI | MR | Zbl
[24] N. Kim, Y. Lee, “Extensions of reversible rings.”, J. Pure Appl. Algebra, 185:1–3 (2003), 207–223 | DOI | MR | Zbl
[25] J. Krempa, “Some examples of reduced rings”, Algebra Colloq., 3:4 (1996), 289–300 | MR | Zbl
[26] J. Lambek, “On the representation of modules by sheaves of factor modules”, Canad. Math. Bull., 14 (1971), 359–368 | DOI | MR | Zbl
[27] O. Lezama, “Computation of point modules of finitely semi-graded rings”, Comm. Algebra, 48:2 (2020), 866–878 | DOI | MR | Zbl
[28] O. Lezama, J. P. Acosta, A. Reyes, “Prime ideals of skew PBW extensions”, Rev. Un. Mat. Argentina, 56:2 (2015), 39–55 | MR | Zbl
[29] O. Lezama, C. Gallego, “$d$-Hermite rings and skew PBW extensions”, São Paulo J. Math. Sci., 10:1 (2016), 60–72 | DOI | MR | Zbl
[30] O. Lezama, J. Gómez, “Koszulity and point modules of finitely semi-graded rings and algebras”, Symmetry, 11:7 (2019), 1–22 | DOI | MR
[31] O. Lezama, E. Latorre, “Non-commutative algebraic geometry of semi-graded rings”, Internat. J. Algebra Comput., 27:4 (2017), 361–389 | DOI | MR | Zbl
[32] O. Lezama, A. Reyes, “Some Homological Properties of Skew PBW Extensions”, Comm. Algebra, 42:3 (2014), 1200–1230 | DOI | MR | Zbl
[33] O. Lezama, H. Venegas, “Center of skew PBW extensions”, Internat. J. Algebra Comput., 30:8 (2020), 1625–1650 | DOI | MR | Zbl
[34] Z. Liu, R. Zhao, “On weak Armendariz rings”, Comm. Algebra, 37:7 (2006), 2607–2616 | DOI | MR
[35] M. Louzari, A. Reyes, “Minimal prime ideals of skew PBW extensions over 2-primal compatible rings”, Rev. Colombiana Mat., 54:1 (2020), 39–63 | DOI | MR | Zbl
[36] G. Marks, “A taxonomy of 2-primal rings”, J. Algebra, 266:2 (2003), 494–520 | DOI | MR | Zbl
[37] J. C. McConnell, J. C. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, AMS, 2001 | DOI | MR | Zbl
[38] A. Moussavi, E. Hashemi, “On $(\alpha,\delta)$-skew Armendariz rings”, J. Korean Math. Soc., 42:2 (2005), 353–363 | DOI | MR | Zbl
[39] A. Niño, M. C. Ramírez, A. Reyes, “Associated prime ideals over skew PBW extensions”, Comm. Algebra, 48:12 (2020), 5038–5055 | DOI | MR | Zbl
[40] A. Niño, A. Reyes, “Some remarks about minimal prime ideals of skew PBW extensions”, Algebra Discrete Math., 30:2 (2020), 207–229 | DOI | MR | Zbl
[41] O. Ore, “Theory of Non-Commutative Polynomials”, Ann. of Math. (2), 34:3 (1933), 480–508 | DOI | MR | Zbl
[42] L. Ouyang, H. Chen, “On weak symmetric rings”, Comm. Algebra, 38 (2010), 697–713 | DOI | MR | Zbl
[43] M. B. Rege, S. Chhawchharia, “Armendariz rings”, Proc. Japan Acad. Ser. A Math. Sci., 73:1 (1997), 14–17 | DOI | MR | Zbl
[44] A. Reyes, “Skew PBW extensions of Baer, quasi-Baer, p.p. and p.q.-rings”, Rev. Integr. Temas Mat., 33:2 (2015), 173–189 | DOI | MR | Zbl
[45] A. Reyes, C. Rodríguez, “The McCoy condition on Skew Poincaré-Birkhoff-Witt Extensions”, Commun. Math. Stat., 9:1 (2021), 1–21 | DOI | MR | Zbl
[46] A. Reyes, H. Suárez, “PBW bases for some 3-dimensional skew polynomial algebras”, Far East J. Math. Sci., 101:6 (2017), 1207–1228 | Zbl
[47] A. Reyes, H. Suárez, “$\sigma$-PBW Extensions of Skew Armendariz Rings”, Adv. Appl. Clifford Algebr., 27:4 (2017), 3197–3224 | DOI | MR | Zbl
[48] A. Reyes, H. Suárez, “A notion of compatibility for Armendariz and Baer properties over skew PBW extensions”, Rev. Un. Mat. Argentina, 59:1 (2018), 157–178 | MR | Zbl
[49] A. Reyes, H. Suárez, “Skew Poincaré-Birkhoff-Witt extensions over weak zip rings”, Beitr. Algebra Geom., 60:2 (2019), 190–216 | DOI | MR
[50] A. Reyes, H. Suárez, “Radicals and Köthe's conjecture for skew PBW extensions”, Commun. Math. Stat., 9:2 (2021), 119–138 | DOI | MR | Zbl
[51] A. Rosenberg, Non-commutative Algebraic Geometry and Representations of Quantized Algebras, Mathematics and Its Applications, 330, Kluwer Academic Publishers, 1995 | MR
[52] H. Suárez, “Koszulity for graded skew PBW extensions”, Comm. Algebra, 45:10 (2017), 4569–4580 | DOI | MR | Zbl
[53] H. Suárez, O. Lezama and A. Reyes, “Calabi-Yau property for graded skew PBW extensions”, Rev. Colombiana Mat., 51:2 (2017), 231–238 | MR
[54] A. B. Tumwesigye, J. Richter, S. Silvestrov, “Centralizers in PBW Extensions”, Algebraic Structures and Applications, SPAS 2017, Springer Proceedings in Mathematics Statistics, 317, eds. Silvestrov S., Malyarenko A., Rancić M., Springer, Cham, 2020 | MR
[55] B. A. Zambrano, “Poisson brackets on some skew PBW extensions”, Algebra Discrete Math., 29:2 (2020), 277–302 | DOI | MR | Zbl