摘要
首先给出环R成为域的一个充分必要条件 ,然后给出域的加群自同态成为域自同态的充分必要条件。
In this paper,we obtain the following results:1 Let R be a ring,then R is a field if and only if R[x] is a principal ideal domain,2 Let F be a field , f∈END(f,+) ,then f is a endomorphism of F as a field if and only if it satisfies the conditions: (1)f(1)=1,(2)f(α)f(α -1 )=1,α∈F *.
