摘要
For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm（N）Mm（R） is quasi-Armendariz if and only if Tm（N）Tm（R） is quasi-Armendariz, where Mm（N） and Tm（N） denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.
For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm（N）Mm（R） is quasi-Armendariz if and only if Tm（N）Tm（R） is quasi-Armendariz, where Mm（N） and Tm（N） denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.
基金
Supported by the National Natural Science Foundation of China (Grant No.10571026)
the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20060286006)
Science Foundation for Youth Scholars of Northwest Normal University (Grant No.NWNU-LKQN-08-1)
