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中文摘要：
通过将箭图的每个顶点放置一个k-余代数，首先引进了广义路余代数的概念，其次给出了广义路余代数的一些基本性质，还讨论了同构问题．证明了两个正规广义路余代数是同构的当且仅当他们的箭图及对应顶点上的单余代数是同构的．对于满足Codim Co≤1余代数C，证明了对偶Wedderburn-Malcev定理成立．作为广义路余代数的一个应用，推广了点余代数的对偶Gabriel定理．
英文摘要：
We firstly introduce the concept of generalized path coalgebra through assigning a k-coalgebra to each vertex of a given quiver. Then some elementary properties of generalized path coalgebras are given. Moreover, we discuss the isomorphism problem. It is shown that two normal generalized path coalgebras are isomorphic if and only if their quivers and the simple coalgebras over the corresponding vertices are isomorphic. For a coalgebra with Codim Co ≤ 1, the Wedderburn-Malcev Theorem is proven. As an application of the generalized path coalgebras, the Dual Gabriel Theorem for pointed coalgebras is generalized.
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