In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.展开更多
The article presents an original concept of a universal philosophical language capable of transcending the boundaries between individual sciences and serving as a foundation for transdisciplinary thinking.This approac...The article presents an original concept of a universal philosophical language capable of transcending the boundaries between individual sciences and serving as a foundation for transdisciplinary thinking.This approach,developed by the author since the 1980s,is based on particular and general comparative concepts-concepts of practical mind and categories of pure mind.Therefore,the key element of the concept is the category of"particular and general",which fundamentally differs from the traditional category of"part and whole".This allows for the description of both structural and functional aspects of complex systems not only at the interdisciplinary but also at the transdisciplinary level.The primary categories of thought-Identity,Difference,Correlated,Opposite,and others-are regarded as universal notions that connect levels of reality and ensure the integration of individual sciences.Unlike contemporary transdisciplinary concepts based on Basarab Nicolescu's logic of the included middle and Edgar Morin's dialogics,the author's theory is built on the ultimate general Hegelian notion of"concrete identity"and its differentiation into a multitude of"concrete differences"-comparative concepts.As a result,a unique philosophical language has been developed,presented within the framework of the Philosophical Matrix as a system of categories of pure mind capable of describing the dynamics and wholeness of complex processes at the transdisciplinary level.The article is intended for researchers interested in the philosophical foundations of transdisciplinarity,the theory of complexity,and the development of universal categories of thought.展开更多
Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein hom...Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein homological dimensions and the Auslander categories of R.展开更多
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
文摘The article presents an original concept of a universal philosophical language capable of transcending the boundaries between individual sciences and serving as a foundation for transdisciplinary thinking.This approach,developed by the author since the 1980s,is based on particular and general comparative concepts-concepts of practical mind and categories of pure mind.Therefore,the key element of the concept is the category of"particular and general",which fundamentally differs from the traditional category of"part and whole".This allows for the description of both structural and functional aspects of complex systems not only at the interdisciplinary but also at the transdisciplinary level.The primary categories of thought-Identity,Difference,Correlated,Opposite,and others-are regarded as universal notions that connect levels of reality and ensure the integration of individual sciences.Unlike contemporary transdisciplinary concepts based on Basarab Nicolescu's logic of the included middle and Edgar Morin's dialogics,the author's theory is built on the ultimate general Hegelian notion of"concrete identity"and its differentiation into a multitude of"concrete differences"-comparative concepts.As a result,a unique philosophical language has been developed,presented within the framework of the Philosophical Matrix as a system of categories of pure mind capable of describing the dynamics and wholeness of complex processes at the transdisciplinary level.The article is intended for researchers interested in the philosophical foundations of transdisciplinarity,the theory of complexity,and the development of universal categories of thought.
基金Supported by the National Natural Science Foundation of China(Grant No.11261050)
文摘Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein homological dimensions and the Auslander categories of R.
