查看更多>>摘要：Let R be a ring with an endomorphism σ,FU {0} the free monoid generated by U={u1,...,ut} with 0 added,and M a factor of F obtained by setting certain monomials in F to 0 such that Mn=0 for some n.Then we can form the non-semiprime skew monoid ring R[M;σ].A local ring R is called bleached if for any j ∈ J(R)and any u ∈ U(R),the abelian group endomorphisms lu-rj and lj-ru of R are surjective.Using R[M;σ],we provide various classes of both bleached and non-bleached local rings.One of the main problems concerning strongly clean rings is to characterize the rings R for which the matrix ring Mn(R)is strongly clean.We investigate the strong cleanness of the full matrix rings over the skew monoid ring R[M;σ].
查看更多>>摘要：Suppose that L is a Lie superalgebra over a field F of characteristic different from 2 and 3.In this paper,the so-called 5-sequence of cohomology for a central extension of L is constructed and is proved to be exact.Moreover,the multiplier of L is proved to be isomorphic to the second cohomology group with coefficients in the trivial module of L.Finally,an upper bound of the superdimension of the second cohomology group is given in the situation when L is nilpotent and finite-dimensional.
查看更多>>摘要：Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classes ξ with enough ξ-projectives and ξ-injectives.Assume that ξ:=ξx=ξy is the proper class induced by a balanced pair(X,y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=y=0,and that(C,Eξ,sξ)is an exact category if and only if X=y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.
查看更多>>摘要：In this paper,we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras.This approach also allows us to calculate the structure constants of multiplication over the Grothendieck ring of the sequence.
查看更多>>摘要：The inclusion ideal graph In(S)of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I,J are adjacent if and only if either I ⊂ J or J ⊂ I.The purpose of this paper is to study algebraic properties of the semigroup S as well as graph theoretic properties of In(S).We investigate the connectedness of In(S)and show that the diameter of In(S)is at most 3 if it is connected.We also obtain a necessary and sufficient condition of S such that the clique number of In(S)is the number of minimal left ideals of S.Further,various graph invariants of In(S),viz.perfectness,planarity,girth,etc.,are discussed.For a completely simple semigroup S,we investigate properties of In(S)including its independence number and matching number.Finally,we obtain the automorphism group of In(S).
查看更多>>摘要：In this note,the compatible left-symmetric superalgebra structures on an infinite-dimensional Lie superalgebra with some natural grading conditions are completely determined.The results of earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures.
查看更多>>摘要：For a ring R(not necessarily commutative)with identity,the comaximal graph of R,denoted by Ω(R),is a graph whose vertices are all the nonunit elements of R,and two distinct vertices a and b are adjacent if and only if Ra+Rb=R.In this paper we consider a subgraph Ω1(R)of S(R)induced by R\Uℓ(R),where Uℓ(R)is the set of all left-invertible elements of R.We characterize those rings R for which Ω1(R)\J(R)is a complete graph or a star graph,where J(R)is the Jacobson radical of R.We investigate the clique number and the chromatic number of the graph Q1(R)\ J(R),and we prove that if every left ideal of R is symmetric,then this graph is connected and its diameter is at most 3.Moreover,we completely characterize the diameter of Ω1(R)\J(R).We also investigate the properties of R when Ω1(R)is a split graph.
查看更多>>摘要：It was shown recently that the heart of a twin cotorsion pair on an extriangu-lated category is semi-abelian.In this article,we consider a special class of hearts of twin cotorsion pairs induced by d-cluster tilting subcategories in extriangulated categories.We give a necessary and sufficient condition for such hearts to be abelian.In particular,we can also see that such hearts are hereditary.As an application,this generalizes the work by Liu in the exact case,thereby providing new insights into the triangulated case.
查看更多>>摘要：Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix Wv of H for tensor-ing with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of Wv are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for Wv by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteris-tic polynomial and eigenvalues of Wv and give all eigenvectors of each eigenvalue for Wv when G is a dihedral group of order 4N+2.
查看更多>>摘要：Let R be a commutative ring with nonzero identity and n be a positive integer.In this paper,we introduce and investigate a new subclass of φ-n-absorbing primary ideals,which are called φ-(n,N)-ideals.Let φ:J(R)→ J(R)U {Ø} be a function,where J(R)denotes the set of all ideals of R.A proper ideal I of R is called a φ-(n,N)-ideal if x1 … xn+1 ∈ I\φ(I)and x1…xn ∉ I imply that the product of xn+1 with(n-1)of x1,...,xn is in √0 for all x1,...,xn+1 ∈ R.In addition to giving many properties ofφ-(n,N)-ideals,we also use the concept of φ-(n,N)-ideals to characterize rings that have only finitely many minimal prime ideals.
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