拟—弱McCoy环

On quasi-weak McCoy rings

引入拟-McCoy环和拟-弱McCoy环并研究其性质.讨论拟-McCoy环和拟-弱McCoy环之间的关系.证明了任意环R上的上三角矩阵环T_n(R)(n≥2)及交换的拟-弱McCoy环R上的n阶全矩阵环M_n(R)是拟-弱McCoy环.对于环R的理想I,当I(?)nil(R)时,若R/I是拟-弱McCoy环,则R是拟-弱McCoy环.同时也证明了R是拟-弱McCoy环当且仅当△^(-1)R是拟-弱McCoy环.

Quasi-McCoy rings and quasi-weak McCoy rings were introduced and their properties investigated. The relation between quasi-McCoy rings and quasi-weak McCoy rings was also discussed and it is shown that the upper triangular matrix rings Tn （R）（n ≥ 2） over any ring R and n-by-n full matrix rings Mn （R） over commutative quasi-weak McCoy rings R are quasi-weak McCoy. For an ideal I of a ring R satisfying I C nil（R）, if R/I is quasi-weak McCoy, then R is quasi-weak McCoy. It is also shown that R is quasi-weak McCoy if and only if △-1R is quasi-weak McCoy.