Propiedad χ en extensiones PBW torcidas graduadas

Contenido principal del artículo

Autores

Héctor Suárez https://orcid.org/0000-0003-4618-0599
Fabián Anaya
Armando Reyes https://orcid.org/0000-0002-5774-0822

Resumen




En este artículo estudiamos la propiedad χ de álgebras que son extensiones PBW torcidas graduadas. Demostramos que si R = ⊕p≥0Rp es un álgebra noetheriana N-graduada y A = σ(R)⟨x1,...,xn⟩ es una extensión PBW torcida cuasi-conmutativa graduada de R, entonces A satisface χ si y solo si R satisface χ. También damos condiciones suficientes para que una extensión PBW torcida graduada de R satisfaga χ.


 




Palabras clave:

Detalles del artículo

Referencias

[1] M. Artin and W. F. Schelter, “Graded algebras of global dimension 3”, Adv. Math., vol. 66, p. 171-216, 1987.

[2] M. Artin and J. J. Zhang, “Noncommutative projective schemes”, Adv. Math., vol. 109, p. 228-287, 1994.

[3] W. Fajardo, C. Gallego, O. Lezama, A. Reyes, H. Suárez and H. Venegas, Skew PBW extensions: Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications, Algebra and Applications, vol. 28, Springer, Springer International Publishing, 2020.

[4] C. Gallego and O. Lezama, “Gröbner bases for ideals of σ −PBW extensions”, Comm. Algebra, vol. 39, p. 50-75, 2011.

[5] J. A. Gómez y H. Suárez, “Algunas propiedades homológicas del plano de Jordan", Ciencia En Desarrollo, vol. 9, no. 2, p. 69-82, 2018.

[6] J. Y. Gómez and H. Suárez, “Double Ore extensions versus graded skew PBW extensions”, Comm. Algebra, vol. 48, no. 1, p. 185-197, 2020.

[7] N. R. González y Y. P. Suárez, “Ideales en el anillo de polinomios torcidos R[x; σ , δ ]", Ciencia En Desarrollo, vol. 5, no. 1, p. 31-37, 2014.

[8] K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts, London, second edition, 2004.

[9] M.Hamidizadeh,E.HashemiandA.Reyes,“A classification of ring elements in skew PBW extensions over compatible rings", Int. Electron. J. Algebra, vol. 28, p. 75-97, 2020.

[10] T. Levasseur, “Some properties of non- commutative regular graded rings”, Glasglow Math. J., vol. 34, p. 277-300, 1992.

[11] O. Lezama and E. Latorre, “Non-commutative algebraic geometry of semi-graded rings”, Internat. J. Algebra Comput., vol. 27, no. 4, p. 361-389, 2017.

[12] O. Lezama and A. Reyes, “Some homological properties of skew PBW extensions”, Comm. Algebra, vol. 42, no. 3, p. 1200-1230, 2014.

[13] A. Reyes and H. Suárez, “Some remarks about the cyclic homology of skew PBW extensions", Ciencia En Desarrollo, vol. 7, no. 2, p. 99-107, 2016.

[14]A. Reyes and H. Suárez, “Radicals and Köthe’s conjecture for skew PBW extensions”, Commun. Math. Stat., 2019, https://doi.org/10.1007/s40304-019-00189-0

[15]A. Reyes and H. Suárez, “Skew Poincaré- Birkhoff-Witt extensions over weak compatible rings”, J. Algebra Appl., vol. 19, no. 12, p. 2050225(1)-2050225(21), 2020.

[16]A. Reyes and H. Suárez, “Skew Poincaré- Birkhoff-Witt extensions over weak zip rings”, Beitr. Algebra Geom., vol. 60, p. 197-216, 2019.

[17]L. Salcedo, “Hopf algebras and skew PBW extensions”, Ciencia En Desarrollo, vol. 10, no. 2, p. 125-135, 2019.

[18]H. Suárez, “Koszulity for graded skew PBW extensions”, Comm. Algebra, vol. 45, no. 10, p. 4569-4580, 2017.

[19]H. Suárez, O. Lezama and A. Reyes, “Some relations between N-Koszul, Artin-Schelter regular and Calabi-Yau algebras with skew PBW extensions”, Ciencia En Desarrollo, vol. 6, no. 2, p. 205-213, 2015.

[20]H. Suárez, O. Lezama and A. Reyes, “Calabi- Yau property for graded skew PBW extensions”, Rev. Colombiana Mat., vol. 51, no. 2, p. 221-238, 2017.

[21]H. Suárez and A. Reyes, “Nakayama automorphism of some skew PBW extensions”, Ingeniería y Ciencia, vol. 15, no. 29, p. 157-177, 2019.

Descargas

La descarga de datos todavía no está disponible.