2019/08/13 by Oswaldo Lezama, Lezama, Oswaldo
Mathematics · #16D40 #16E05 #16E65 #16S38 #16S80 #16W70 #16Z05 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Primary: 16S36. Secondary: 16U20 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1908.04880
openalex publication_date 2019/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss some open problems of non-commutative algebra and\nnon-commutative algebraic geometry from the approach of skew PBW extensions\nand semi-graded rings. More exactly, we will analyze the isomorphism arising in\nthe investigation of the Gelfand-Kirillov conjecture about the commutation\nbetween the center and the total ring of fractions of an Ore domain. The\nSerre's conjecture will be discussed for a particular class of skew PBW\nextensions. The questions about the noetherianity and the Zariski cancellation\nproperty of Artin-Schelter regular algebras will be reformulated for\nsemi-graded rings. Advances for the solution of some of the problems are\nincluded.\n