摘要
R是主理想整环,a是R中固定的元素。本文证明了:当n是偶数时,对任意A∈Mn(R),存在X,Y∈Mn(R),使得X+Y=A且det(X)=det(Y)=a。当n是奇数时,对任意A∈Mn(R),存在X,Y∈Mn(R),使得X+Y=A且det(X)=det(Y)=a当且仅当d(A)|2a。
R be a a principle ideal domain and a fixed element in R.This paper proved that if nbe an integer, then for any A in Mn(R) there are X, Y in Mn(R) with det(X) =det(Y)=a,such that X+Y=A. If n be an old integer, then for any A in Mn(R) there are X, Y in Mn(R)withdet(X)=det(Y) = a such that X+Y=A if and only if d(A) divides 2a.
