Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutio...Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of （a, b, c, d）-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be （a, b, c, d）- Koszul are provided.展开更多
We prove an Artin-Schelter regularity result for the method of twisted tensor products under a certain form. Such twisted tensor products, whose twisting maps are determined by the action on the generators, include Or...We prove an Artin-Schelter regularity result for the method of twisted tensor products under a certain form. Such twisted tensor products, whose twisting maps are determined by the action on the generators, include Ore extensions and double Ore extensions. It is helpful to construct high- dimensional Artin-Schelter regular algebras.展开更多
基金Supported by the NSFC (10771112)NSF of Shandong Province (Y2008A05)
文摘Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11571316, 11001245） and the Natural Science Foundation of Zhejiang Province （Grant No. LY16A010003）.
文摘Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of （a, b, c, d）-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be （a, b, c, d）- Koszul are provided.
文摘We prove an Artin-Schelter regularity result for the method of twisted tensor products under a certain form. Such twisted tensor products, whose twisting maps are determined by the action on the generators, include Ore extensions and double Ore extensions. It is helpful to construct high- dimensional Artin-Schelter regular algebras.
