查看更多>>摘要：We define the cohomology of associative H-pseudoalgebras,and we show that it describes module extensions,abelian pseudoalgebra extensions,and pseudoalgebra first-order deformations.The same results for the special case of associative conformal algebras are also described in details.
查看更多>>摘要：We extend the notions of commutativity,ideals,anisotropy,and complemented subtriples of Jordan triple systems to those of Jordan quadruple systems.We show that if S is a complemented subsystem of an anisotropic commutative Jordan quadruple system U,then S and its annihilator S⊥ are orthogonal ideals and U=S ⊕ S⊥.We also prove that the range of a structural projection on an anisotropic commutative Jordan quadruple system is a complemented ideal and,conversely,a complemented subsystem of an anisotropic commutative Jordan quadruple system is the range of a unique structural projection.
查看更多>>摘要：Let R be a commutative ring with identity,M be an R-module,(L)(M)denote the set of all submodules of M and(G)(€)(L)(M)\{OM}.For any submodule N of M,we set(G)Vd(N)={K ∈(G):K(∈) N} and(G)ζd(M)={(G)Vd(N):N ∈(L)(M)}.Consider x ⊆(L)(R)\{R},where(L)(R)is the set of all ideals of R.We set xV(I)={J∈x:I⊆J}and xζ(R)={xV(I):I ∈(L)(R)} for any ideal I of R.In this paper,we investigate when,for arbitrary x and(G)as above,xζ(R)and(G)ζd(M)form a topology and a semimodule,respectively.We investigate the structure of(G)ζd(M)in the case that it is a semimodule.
查看更多>>摘要：Let R be a unital*-ring.For any a,w,b ∈ R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b ∈ R are w-core invertible.We say that a is below b under the w-core partial order if a(#)w a=a(#)w b and awa(#)w=bwa(#)w,where a(#)w denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.
查看更多>>摘要：Over a field of characteristic p＞2,the first cohomology of the orthogonal symplectic Lie superalgebra osp(1,2)with coefficients in baby Verma modules and simple modules is determined by use of the weight space decompositions of these modules relative to a Cartan subalgebra of osp(1,2).As a byproduct,the first cohomology of osp(1,2)with coefficients in the restricted enveloping algebra(under the adjoint action)is not trivial.
查看更多>>摘要：We introduce the notion of a quadratic graph,which is a graph whose eigen-values are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including inte-gral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.
查看更多>>摘要：Let(G)n([-1]i)denote the set of all connected graphs on n vertices having distance eigenvalue-1 of multiplicity i.By using the distribution of the third largest distance eigenvalue and the second least distance eigenvalue of a connected graph,in this paper we completely characterize the graphs in(G)n([-1]i),where i=n-1,n-2,n-3 or n-4.
查看更多>>摘要：Let t be any positive integer and I(Cn)the edge ideal of a vertex-weighted oriented n-cycle graph Cn.We provide explicit formulas for the regularity and depth of I(Cn)t.In particular,we find that the regularity of I(Cn)t is a linear function;Ass(I(Cn)t),the set of associated prime ideals of I(Cn)t,equals Ass(I(Cn));and the depth of I(Cn)t is a constant for all t.We also give some examples to show that these results are related to the direction selection of edges and the weight of vertices.
查看更多>>摘要：Let(A,B,C)be a recollement of extriangulated categories.In this paper we introduce the global dimension and extension dimension of extriangulated categories,and give some upper bounds of global dimensions and extension dimensions of the cat-egories involved in(A,B,C),which give a simultaneous generalization of some results in recollements of abelian categories and triangulated categories.
查看更多>>摘要：In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is the direct sum of two vector spaces which are also Bihom-subalgebras.Then we give four special conditions under each of which a 3-Bihom-Lie algebra has a special decomposition.Similarly,we introduce a com-plex structure on a 3-Bihom-Lie algebra and there are also four types of special complex structures.Finally,we establish the relation between a complex structure and a product structure.
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