中文摘要：

设A是一个域k上的基本有限维代数.本文证明了如果AT是一个n-BB-倾斜模,那么TB亦为n-BB-倾斜模,其中B=End（AT）.进一步,如果AT是一个n-APR-倾斜模,那么TB亦为n-APR-倾斜模.最后,把本文的结果应用到一个具有n-APR-倾斜模AT的代数A上,得到A是n-表示-有限的（无限的）当且仅当B是n-表示-有限的（无限的）.

英文摘要：

Let A be a basic finite dimensional Mgebra over some field k. In this paper, we prove that if AT is an n-BB-tilting module, then TB is also an n-BB-tilting module, where B=End（AT）. Furthermore, if AT is an n-APR-tilting module, then TB is also an n-APR-tilting module. Finally, applying our results to an algebra A which admits an n-APR-tilting module AT, we obtain that A is n-representation-finite （infinite） if and only if B is n-representation- finite （infinite）.