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	1. On Auslander-Type Conditions of Modules
	Huang Zhaoyong
	Mathematics 22 October 2013
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	Abstract:We prove that for a left and right Noetherian ring $R$, $_RR$satisfies the Auslander condition if and only if so does every flatleft $R$-module, if and only if the injective dimension of the $i$thterm in a minimal flat resolution of any injective left $R$-moduleis at most $i-1$ for any $i geq 1$, if and only if the flat (resp.injective) dimension of the $i$th term in a minimal injective (resp.flat) resolution of any left $R$-module $M$ is at most the flat(resp. injective) dimension of $M$ plus $i-1$ for any $i geq 1$, ifand only if the flat (resp. injective) dimension of the injectiveenvelope (resp. flat cover) of any left $R$-module $M$ is at mostthe flat (resp. injective) dimension of $M$, and if and only if anyof the opposite versions of the above conditions hold true.Furthermore, we prove that for an Artinian algebra $R$ satisfyingthe Auslander condition, $R$ is Gorenstein if and only if thesubcategory consisting of finitely generated modules satisfying theAuslander condition is contravariantly finite.As applications, we get some equivalentcharacterizations of Auslander-Gorenstein rings andAuslander-regular rings.
	TO cite this article:Huang Zhaoyong. On Auslander-Type Conditions of Modules[OL].[22 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4565403


	2. Representations of Lie conformal algebra of Block type
	GAO Ming,XU Ying,YUE Xiaoqing
	Mathematics 29 August 2013
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	Abstract:Let L be a Lie algebra of Block type over C with basis {Lα,i,\|α,i∈Z} and brackets [Lα,i,Lβ,j]=(β(i+1)-α(j+1))Lα+β,i+j. In this paper, we shall construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B. Finally, we give a classification of free intermediate series B-modules.
	TO cite this article:GAO Ming,XU Ying,YUE Xiaoqing. Representations of Lie conformal algebra of Block type[OL].[29 August 2013] http://en.paper.edu.cn/en_releasepaper/content/4557453

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	3. On two open problems of Mahmoudi and Renshaw
	Qiao Husheng,Wei Chongqing
	Mathematics 07 December 2012
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	Abstract:This paper continues the investigation of covers of cyclic acts overmonoids. Special attention is paid to (P)-covers and strongly flatcovers of cyclic acts. We give some examples to show that thereexists a monoid S and a cyclic S-act A which does not have a(P)-cover, and there exists a monoid S and a cyclic S-act A such that the strongly flat covers of A is not unique. Hence weanswer the open problems 1 and 5 in [1].
	TO cite this article:Qiao Husheng,Wei Chongqing. On two open problems of Mahmoudi and Renshaw[OL].[ 7 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4500624


	4. Lie conformal algebras with filtration
	SU Yucai,YUE Xiaoqing
	Mathematics 13 April 2012
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	Abstract:Let G be a filtered Lie conformal algebra whose associatedgraded conformal algebra is isomorphic to that of general conformalalgebra gc1. In this paper, we prove that G is either isomorphic to gc1 or to the associatedgraded conformal algebra of gc1. Furthermore, we prove thatthe associatedgraded conformal algebra of gc1 does not have a nontrivial representation on a finite C[δl]-module, this provides animportant example of a finitely freely generated simple Lie conformal algebra of lineargrowth that cannot be embedded into the general conformal algebra gcN for any N.
	TO cite this article:SU Yucai,YUE Xiaoqing. Lie conformal algebras with filtration[OL].[13 April 2012] http://en.paper.edu.cn/en_releasepaper/content/4473817


	5. Representations of Lie algebras B(q) of Block type
	SU Yucai,XIA Chunguang,XU Ying
	Mathematics 30 March 2012
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	Abstract:Intrigued by a well-known theorem ofMathieu's on Harish-Chandra modules over the Virasoro algebra, weshow that any quasifinite irreducible module over a class of Blocktype Lie algebras B(q) is either a highest or lowest weight module, or elsea uniformly bounded module, where the parameter q is a nonzero complexnumber. We also classify quasifinite irreducible highest weightB(q)-modules and irreducible B(q)-modules of the intermediateseries. In particular, we obtain that an irreducible B(q)-module ofthe intermediate series may be a nontrivial extension of aVir-module of the intermediate series if q is half of anegative integer, where Vir is a subalgebra of B(q) isomorphicto the Virasoro algebra.
	TO cite this article:SU Yucai,XIA Chunguang,XU Ying. Representations of Lie algebras B(q) of Block type[OL].[30 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4473607


	6. Leibniz 2-algebras and twisted Courant algebroids
	Sheng Yunhe ,Liu Zhangju
	Mathematics 12 March 2012
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	Abstract: In this paper, the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras is given.They reveal the algebraic structure of omni-Lie 2-algebras as well as twisted Courant algebroidsby closed 4-forms. Dirac structures of twisted Courant algebroids give rise to 2-term L∞-algebras and geometric structures behind them areexactly H-twisted Lie algebroids
	TO cite this article:Sheng Yunhe ,Liu Zhangju . Leibniz 2-algebras and twisted Courant algebroids[OL].[12 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4468380


	7. Cyclic and 1-generator quasi-cyclic codes over F_q+uF_q
	ZHU Shixin,KAI Xiaoshan,XU Xianqi
	Mathematics 15 February 2012
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	Abstract:In this paper, we study cyclic codes and 1-generator quasi-cyclic codes over the ring F_q+uF_q where q is a prime power and u^2=0. We give generator polynomials of cyclic codes over F_q+uF_q and discuss some Gray maps on F_q+uF_q. These results are used to study the structure of 1-generator quasi-cyclic codes over F_q+uF_q. A lower bound on Gray distance for a class of 1-generator quasi-cyclic codes over F_q+uF_q is obtained.
	TO cite this article:ZHU Shixin,KAI Xiaoshan,XU Xianqi. Cyclic and 1-generator quasi-cyclic codes over F_q+uF_q[OL].[15 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4466661


	8. The Representations of Quantum Double of DihedralGroups
	Dong Jingcheng,CHEN Huixiang
	Mathematics 14 February 2012
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	Abstract:Let k be an algebraically closed field ofodd characteristic p, and let Dn be the Dihedral group of order2n such that pmid 2n. Let D(kDn) denote the quantum doubleof the group algebra kDn. In this paper, thestructures of all finite dimensional indecomposable leftD(kDn)-modules are described and classified, equivalently, all finite dimensionalindecomposable Yetter-Drinfeld kDn-modules are described, and classified.
	TO cite this article:Dong Jingcheng,CHEN Huixiang. The Representations of Quantum Double of DihedralGroups[OL].[14 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4466399


	9. Yetter-Drinfeld Modules over The Hopf Ore Extension of The Group Algebra of Dihedral Group
	ZHU Hong,CHEN Huixiang
	Mathematics 14 February 2012
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	Abstract:Let k be an algebraically closed field of characteristic zero, and Dn be the dihedral groupof order 2n, where n is a positive even integer. In this paper, the Yetter-Drinfeld modulesover the Hopf-Ore extension A(n,0) of kDn are investigated. The the structures and properties of simpleYetter-Drinfeld modules over A(n,0) are described, and all simple Yetter-Drinfeld modules over A(n,0) areclassified up to isomorphism.
	TO cite this article:ZHU Hong,CHEN Huixiang. Yetter-Drinfeld Modules over The Hopf Ore Extension of The Group Algebra of Dihedral Group[OL].[14 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4466396


	10. On an infinite-dimensional Lie algebra of Virasoro-type
	PEI Yufeng ,BAI Chengming
	Mathematics 13 December 2011
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	Abstract:In this paper, we study an infinite-dimensional Lie algebra of Virasoro-type whichis realized as an affinization of a 2-dimensional Novikov algebra. It is a special deformation ofthe Liealgebra of differential operators on a circle of order at most one.There is an explicit construction of a vertex algebra associated to the Lie algebra.We determine derivations and central extensionsof this Lie algebra in terms of derivations and bilinear formsof the corresponding Novikov algebra respectively.
	TO cite this article:PEI Yufeng ,BAI Chengming. On an infinite-dimensional Lie algebra of Virasoro-type[OL].[13 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4454969

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