部分倾斜模和无短循环的模范畴  

Partial Tilting Module and Module Categories Without Short Cycles

作　　者：师钦贤[1] 李思泽[1] 刘艳杰[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《北方交通大学学报》2003年第6期83-85,共3页Journal of Northern Jiaotong University

摘　　要：令Λ为Artin代数,定义满足投射维数小于等于1且一次扩张函数是0的模为部分倾斜模.文中指出一个模在短循环中等价于它在短链中,并从这一事实出发给出了在一定条件下部分倾斜模的判定定理.得出的主要结果有:X和M是无短循环的模范畴中的不可分解模.若M为忠实Λ模,则M是部分倾斜模.进一步,若存在从X到M的非零态射,则X也是部分倾斜模.Let Λ be Artin algebra, partial tilting module is defined by projective dimension less than 1 and the first tensor equals to 0. Then a module is the middle term of a short chain equaling to lying in a short cycle, which can be used to prove some theorems of partial tilting modules. The main conclusion of this article is M and X are indecomposable modules in module categories without short cycles. If M is sincere module, then M is partial tilting module. Moreover, if there exists nonzero morphism from X to M, then X is also partial tilting module.

关 键 词：模论 短循环 忠实模 部分倾斜模 

分 类 号：O152.6[理学—数学]