查看更多>>摘要：For a local commutative Gorenstein ring R,Enochs et al.in[Gorenstein pro-jective resolvents,Comm.Algebra 44(2016)3989-4000]defined a functor(^)ExtRn(-,-)and showed that this functor can be computed by taking a totally acyclic complex arising from a projective coresolution of the first component or a totally acyclic complex arising from a projective resolution of the second component.In order to define the functor(^)ExtRn(-,-)over general rings,we introduce the right Gorenstein projective dimension of an R-module M,RGpd(M),via Gorenstein projective coresolutions,and give some equivalent char-acterizations for the finiteness of RGpd(M).Then over a general ring R we define a co-Tate homology group(^)ExtRn(M,N)for R-modules M and N with RGpd(M)＜∞ and Gpd(N)＜∞,and prove that(^)ExtRn(M,N)can be computed by complete projective cores-olutions of the first variable or by complete projective resolutions of the second variable.
查看更多>>摘要：The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called right exp-DR.We investigate the structures of group rings,right quotient rings,matrix rings and(skew)polynomial rings,through the study of right exp-DR rings.In addition,we provide a method of constructing finite non-abelian p-groups for any prime p.
查看更多>>摘要：We aim to study maximal pairwise commuting sets of 3-transpositions(trans-vections)of the simple unitary group Un(2)over GF(4),and to construct designs from these sets.Any maximal set of pairwise commuting 3-transpositions is called a basic set of transpositions.Let G=Un(2).It is well known that G is a 3-transposition group with the set D,the conjugacy class consisting of its transvections,as the set of 3-transpositions.Let L be a set of basic transpositions in D.We give general descriptions of L and 1-(v,k,λ)designs D=(P,B),with P=D and B={Lg | g ∈ G}.The parameters k=|L|,λ and further properties of D are determined.We also,as examples,apply the method to the unitary simple groups U4(2),U5(2),U6(2),U7(2),U8(2)and U9(2).
查看更多>>摘要：In the Ringel-Hall algebra of Dynkin type,the set of all commutator rela-tions between the isoclasses of indecomposable representations forms a minimal Gröbner-Shirshov basis and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel-Hall algebra.We aim to generalize this result to the reduced Drinfeld double Hall algebra of type An.First,we compute a minimal Gröbner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compo-sitions between the commutator relations are trivial.Then,by taking the corresponding irreducible monomials,we construct a PBW-type basis for the reduced Drinfeld double Hall algebra of type An.
查看更多>>摘要：This paper introduces the notion of depth with respect to ideals for unbounded DG-modules,and gives a reduction formula and the local nature of this depth.As applica-tions,we provide several bounds of the depth in special cases,and recover and generalize the known results about the depth of complexes.In addition,the width with respect to ideals for unbounded DG-modules is investigated and the depth and width formulas for DG-modules are generalized.
查看更多>>摘要：Jordan D-bialgebras were introduced by Zhelyabin.In this paper,we use a new approach to study Jordan D-bialgebras by a new notion of the dual representation of the regular representation of a Jordan algebra.Motivated by the essential connection between Lie bialgebras and Manin triples,we give an explicit proof of the equivalence between Jor-dan D-bialgebras and a class of special Jordan-Manin triples called double constructions of pseudo-euclidean Jordan algebras.We also show that a Jordan D-bialgebra leads to the Jordan Yang-Baxter equation under the coboundary condition and an antisymmetric non-degenerate solution of the Jordan Yang-Baxter equation corresponds to an antisymmetric bilinear form,which we call a Jordan symplectic form on Jordan algebras.Furthermore,there exists a new algebra structure called pre-Jordan algebra on Jordan algebras with a Jordan symplectic form.
查看更多>>摘要：The spectra of generalized Cayley graphs of finite abelian groups are investi-gated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X x K2.In this paper,integral generalized Cayley graphs on finite abelian groups are characterized,using the characterization of the spectra of integral Cayley graphs.As an application,the integral generalized Cayley graphs on Zp×Zq and Z2n are investigated,where p and q are odd prime numbers.
查看更多>>摘要：Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's crite-rion,we study the permutational properties of the reversed Dickson polynomials Dn,k(1,x)over finite fields in the case of n=mps with 0＜m＜p-1.In particular,we provide some precise characterizations for Dn,k(1,x)being permutation polynomials over finite fields with characteristic p when n=2ps,or n=3ps,or n=4ps.
查看更多>>摘要：A set{a1,a2,...,am}of positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all 1≤i＜j≤m.Let{a,b,c}be the Diophantine triple with c＞max{a,b}.In this paper,we find the condition for the reduction of third element c,and using this result,we prove the extendibility of Diophantine pair{Fk-1Fk+1,Fk-2Fk+2},where Fn is the n-th Fibonacci number.
查看更多>>摘要：Extriangulated categories were introduced by Nakaoka and Palu via extract-ing the similarities between exact categories and triangulated categories.In this article we introduce the notion of ξ-tilting objects in an extriangulated category,where ξ is a proper class of E-triangles.Our results extend the relative tilting theory in extriangulated categories.
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