The author studies the stabilization for the unitary groups over polynomial rings and obtainsfor them some results analogous to the results of linear groups and symplectic groups.It isespecially proved that K1 U(A) = ...The author studies the stabilization for the unitary groups over polynomial rings and obtainsfor them some results analogous to the results of linear groups and symplectic groups.It isespecially proved that K1 U(A) = K1 U(R) where A = R[X1,…, Xm], R is a ring of algebraicintegers in a quadratic field Q().展开更多
We study the right duo property on regular elements,and we say that rings with this property are right DR.It is first shown that the right duo property is preserved by right quotient rings when the given rings are rig...We study the right duo property on regular elements,and we say that rings with this property are right DR.It is first shown that the right duo property is preserved by right quotient rings when the given rings are right DR.We prove that thepolynomial ring over a ring R is right DR if and only if R is commutative.It is also proved that for a prime number p,the group ring KG of a finite p-group G over a field K of characteristic p is right DR if and only if it is right duo,and that there exists a group ring KG that is neither DR nor duo when G is not a p-group.展开更多
文摘The author studies the stabilization for the unitary groups over polynomial rings and obtainsfor them some results analogous to the results of linear groups and symplectic groups.It isespecially proved that K1 U(A) = K1 U(R) where A = R[X1,…, Xm], R is a ring of algebraicintegers in a quadratic field Q().
文摘We study the right duo property on regular elements,and we say that rings with this property are right DR.It is first shown that the right duo property is preserved by right quotient rings when the given rings are right DR.We prove that thepolynomial ring over a ring R is right DR if and only if R is commutative.It is also proved that for a prime number p,the group ring KG of a finite p-group G over a field K of characteristic p is right DR if and only if it is right duo,and that there exists a group ring KG that is neither DR nor duo when G is not a p-group.
