Right Buchberger Algorithm over Bijective Skew PBW Extensions

• Autorzy: Fajardo William

Identyfikatory

DOI

10.3233/FI-2021-2093

• Języki publikacji: EN

Abstrakty

EN

In this paper we present a right version of the Buchberger algorithm over skew Poincaré-Birkhoff-Witt extensions (skew PBW extensions for short) defined by Gallego and Lezama [5]. This algorithm is an adaptation of the left case given in [3]. In particular, we developed a right version of the division algorithm and from this we built the right Grbner bases theory over bijective skew PBW extensions. The algorithms were implemented in the SPBWE library developed in Maple, this paper includes an application of these to the membership problem. The theory developed here is fundamental to complete the SPBWE library and thus be able to implement various homological applications that arise as result of obtaining the right Grbner bases over skew PBW extensions.

Słowa kluczowe

EN

Non-commutative computational algebra; skew P BW extensions; Buchberger algorithm; Gröbner bases; SPBWE library; Maple

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2021
• Tom: Vol. 184, nr 2
• Strony: 83--105
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Fajardo William

• Seminario de ´Algebra Constructiva - SAC2 Departamento de Matem´aticas Universidad Nacional de Colombia, Bogot´a, Colombia

Bibliografia

• [1] Fajardo W. A computational Maple library for skew PBW extensions, Fundamenta Informaticae, 2019. 176(3):159-191. doi:10.3233/FI-2019-1813.
• [2] Fajardo W, and Lezama O. Elementary matrix-computational proof of Quillen-Suslin for Ore extensions, Fundamenta Informaticae, 2019. 164(1):41-59. doi:10.3233/FI-2019-1754.
• [3] Fajardo W, Gallego C, Lezama O, Reyes A, Suarez H, Vanegas H. Skew P BW extensions, Springer Switzerland AG 2020. ISBN 978-3-030-53377-9.
• [4] Fajardo W. Extended modules over skew P BW extensions. Ph.D. Thesis, Universidad Nacional de Colombia, Bogota, 2018.
• [5] Gallego C, and Lezama O. Gr¨obner bases for ideals of σ-PBW extensions, Comm. Algebra, 2011. 39(1):50-75. doi:10.1080/00927870903431209.
• [6] Gallego C. Matrix methods for projective modules over σ-PBW extensions, Ph.D. Thesis, Universidad Nacional de Colombia, Bogot/’a, 2015.
• [7] Gasiorek M, Simson D, Zajac K. Algorithmic computation of principal posets using Maple and Python, Algebra Discrete Math., 2014. 17(1):33-69. URL http://dspace.nbuv.gov.ua/handle/123456789/152339.
• [8] Lezama O. Gr¨obner bases for modules over Noetherian polynomial commutative rings, Georgian Mathematical Journal, 2008. 15:121-137. doi:10.1515/GMJ.2008.121.
• [9] Lezama O. Anillos dimensionales, Bolet´ın de Matem´aticas, 1985 19:194-220. ISSN-e:0120-0380.
• [10] Adams W, and Loustaunau P. An Introduction to Gr¨obner Bases, Graduate Studies in Mathematics, AMS, 1994. ISBN:978-0-8218-3804-4, 978-1-4704-1139-8.
• [11] Simson D, and Wojewódzky M. An algorithmic solution of a Birkhoff type problem, Fundamenta Informaticae. 2008. 83(4):389-410.
• [12] Simson D. Stanisław Balcerzyk-życie i twórczość, Wiadomości Matematyczne, 2014. 50(2):261-284.
• [13] Simson D. Tame–wild dichotomy of Birkhoff type problems for nilpotent linear operators, J. Algebra 2015. 424:254-293. doi:10.1016/j.jalgebra.2014.11.008.
• [14] Simson D. Representation-finite Birkhoff type problems for nilpotent linear operators, J. Pure Appl. Algebra 2018. 222(8):2181-2198. doi:10.1016/j.jpaa.2017.09.005.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023). (PL)