On the Yoneda Ext-Algebras of Semiperfect Algebras
On the Yoneda Ext-Algebras of Semiperfect Algebras
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DOI：
10.1142/s1005386708000217
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发表时间：
2008-06
影响因子：
0.3
通讯作者：
Ji-wei He;Yu Ye
中科院分区：
文献类型：
--
作者：
Ji-wei He;Yu Ye
It is proved that the Yoneda Ext-algebras of Morita equivalent semiperfect algebras are graded equivalent. The Yoneda Ext-algebras of noetherian semiperfect algebras are studied in detail. Let A be a noetherian semiperfect algebra with Jacobson radical J. We construct a right ideal $\overline{E}(A)$ of the Yoneda algebra $E(A)={\rm Ext}^*_A(A/J,A/J)$, which plays an important role in the discussion of the structure of E(A). An extra grading is introduced to $\overline{E}(A)$, by which we give a description of the right ideal of E(A) generated by ${\rm Ext}^1_A(A/J,A/J)$, and we give a necessary and sufficient condition for a notherian semiperfect algebra to be higher quasi-Koszul. Finally, it is shown that the quasi-Koszulity of a noetherian semiperfect algebra is a Morita invariant.
