| 1. | Then we investigate the minquasi - injective modules with some additional conditions . finally , we study the endomorphism ring on minquasi - injecive modules
其次，我们研究了带有附加条件的min - q -内射模的性质。
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| 2. | They study the duality and selfduality of rings such as extensions of a ring with a morita duality ( or selfduality ) , noether rings , series rings , endomorphism rings and so on
他们研究环扩张， noether环，序列环，自同态环等的对偶性及自对偶。上个世纪九十年代， c menini和a
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| 3. | Especially , we compute the hochschild cohomology of endomorphism algebras of complete exceptional sequence of the path algebra whose quiver has 3 vertices and has no orientation
第四章中，我们主要研究具有三个点的且不带方向圈的有向箭图的路代数上的完备例外序列的自同态代数的hochschild上同调群。
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| 4. | In chapter 3 , we study the property of complete exceptional sequence . in chapter 4 , we make research on the hochschild cohomology of endomorphism algebras of complete exceptional sequence over hereditary algebras
第三章，我们证明了有限维遗传代数中，完备例外序列的维数向量的性质定理以及完备例外序列的诚实性。
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| 5. | In recent years , the endomorphism algebras of complete exceptional sequence of type an and an have been researched . furthermore , the inductive formula of the number of complete exceptional sequence over hereditary algebras of finite representation type has been obtained
对于例外序列自同态代数的研究中，有关a _ n型， a _ n型的完备例外序列的自同态代数的结构都已经清楚，并且进一步得到计算有限表示型遗传代数中完备例外序列个数的递推公式。
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| 6. | We show that near a hyperbolic set a c ~ ( 1 ) endomorphism has the lipschitz shadowing property , and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods . moreover , each of these shadowing properties is also " uniform " with respect to c ~ ( 1 ) perturbation
证明了c ~ 1自同态在其双曲不变集附近具有lipschitz跟踪性，当c ~ 1自同态为双曲时，对一类连续method而言具有反跟踪性，并且这两种跟踪性相对c ~ 1小扰动均具有一致性。
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