一类三阶矩阵环的Armendariz和半交换子环

A Class of Armendariz and Semicommutative Subrings of 3×3 Matrix Rings

考虑环R上三阶矩阵环M3(R)的一类特殊子环S3(R),证明了如果R是reduced环,α,β是R的相容自同态,则S3(R)是半交换Armendariz环,并给出了Armendariz环和半交换环的例子.

We considered a special subring S3（R）of 3×3 matrix ring M3（R）over a ring R.It is shown that S3（R）is an Armendariz and semicommutative ring if R is a reduced ring with compatible endomorphismsα,β.Our results yield more examples of Armendariz rings and semicommutative rings.