In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified m...In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified matrices.展开更多
Let A be a connected cochain DG algebra, whose underlying graded algebra is an Artin-Schelter regular algebra of global dimension 2 generated in degree 1. We give a description of all possible differential of A and co...Let A be a connected cochain DG algebra, whose underlying graded algebra is an Artin-Schelter regular algebra of global dimension 2 generated in degree 1. We give a description of all possible differential of A and compute H（A）. Such kind of DG algebras are proved to be strongly Gorenstein. Some of them serve as examples to indicate that a connected DG algebra with Koszul underlying graded algebra may not be a Koszul DG algebra defined in He and We （J Algebra, 2008, 320： 2934-2962）. Unlike positively graded chain DG algebras, we give counterexamples to show that a bounded below DC A-module with a free underlying graded A^#-module may not be semi-projective.展开更多
基金the National Natural Sciences Foundation of China(10371044)the Science and Technology Commission of Shanghai Municipality through Grant(04JC14031)+1 种基金the University Young Teacher Sciences Foundation of Anhui Province(2006jq1220zd)Supported by the Ph.D.,Program Scholarship Fund of ECNU(2007)
文摘In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified matrices.
基金supported by National Natural Science Foundation of China (Grant No. 11001056)by the China Postdoctoral Science Foundation (Grant No. 20090450066),by the China Postdoctoral Science Foundation (Grant No. 201003244)by Key Disciplines of Shanghai Municipality (Grant No. S30104)
文摘Let A be a connected cochain DG algebra, whose underlying graded algebra is an Artin-Schelter regular algebra of global dimension 2 generated in degree 1. We give a description of all possible differential of A and compute H（A）. Such kind of DG algebras are proved to be strongly Gorenstein. Some of them serve as examples to indicate that a connected DG algebra with Koszul underlying graded algebra may not be a Koszul DG algebra defined in He and We （J Algebra, 2008, 320： 2934-2962）. Unlike positively graded chain DG algebras, we give counterexamples to show that a bounded below DC A-module with a free underlying graded A^#-module may not be semi-projective.
