One-Point Extensions of t-Koszul Algebras
One-Point Extensions of t-Koszul Algebras
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DOI：
10.1007/s10114-007-0903-2
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
Zhi Cheng;Yu Ye
中科院分区：
文献类型：
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作者：
Zhi Cheng;Yu Ye
我们引入了分次模范畴，它是分次代数上分次模的完全子范畴。我们证明了这个子范畴以及由此得到的f-Koszul模的子范畴在单态的扩张和核下都是闭的。研究了单点扩张代数，给出了单点扩张代数为Bet-Koszul的充要条件。我们还考虑了f-Koszul模范畴与二次模范畴重合的条件。
We introduce the category oft-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory oft-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras, and a necessary and sufficient condition for such an algebra to bet-Koszul is given. We also consider the conditions such that the category oft-Koszul modules and the category of quadratic modules coincide.