Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
Let R be a reduced ring,and k,n be integers with 1≤k≤n.We construct a special subring Tk,n(R),relative to endomorphisms of R,of the upper triangular matrix ring Tn(R)over R and show that Tk,n(R)is semicommutative an...Let R be a reduced ring,and k,n be integers with 1≤k≤n.We construct a special subring Tk,n(R),relative to endomorphisms of R,of the upper triangular matrix ring Tn(R)over R and show that Tk,n(R)is semicommutative and Armendariz.Our results yield more examples of semicommutative and Armendariz rings.Also,the maximality of Tk,n(R)in some rings are discussed.展开更多
In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singular...In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring.展开更多
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12161049,12361008).
文摘Let R be a reduced ring,and k,n be integers with 1≤k≤n.We construct a special subring Tk,n(R),relative to endomorphisms of R,of the upper triangular matrix ring Tn(R)over R and show that Tk,n(R)is semicommutative and Armendariz.Our results yield more examples of semicommutative and Armendariz rings.Also,the maximality of Tk,n(R)in some rings are discussed.
基金Supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2025L092)the National Natural Science Foundation of China(Grant No.12071120).
文摘In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring.
