斜三角矩阵环的强可逆性和弱刚性

The Strongly Reversible and Weakly Rigid Properties of Skew Triangular Matrix Rings

设σ是环R的一个自同态,δ是R的一个σ-导子.研究斜三角矩阵环T_(n)(R,α)的强可逆性和(σ,δ)-弱刚性,证明了1)若α是环R的一个刚性自同态,则环R是强可逆环当且仅当T_(n)(R,α)是强可逆环;2)若α和σ都是环R的刚性自同态,ασ=σα,且R是δ-弱刚性环,则R是(σ,δ)-弱刚性环当且仅当T_(n)(R,α)是(σ,δ)-弱刚性环.

Let σ be an endomorphism and δ be an σ-derivation of a ring R.We study in this paper the strongly reversible and(σ,δ)-weakly rigid of skew triangular matrix rings T_(n)(R,α),and show that 1) If α is rigid,then R is strongly reversible if and only if T_(n)(R,α) is strongly reversible;2) If a and σ are all rigid endomorphism of ring R,ασ=σα and R is δ-weakly rigid,then R is(σ,δ)-weakly rigid if and only if T(R,α) is(σ,δ)-weakly rigid.