Let R be an arbitrary ring and (n属于Z+) .If the set Sn is defined bySn = {(a 属于 R) l (n^k) *a = 0 for some k > 0}determine whether Sn is a subring of R.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 01:28:43
![Let R be an arbitrary ring and (n属于Z+) .If the set Sn is defined bySn = {(a 属于 R) l (n^k) *a = 0 for some k > 0}determine whether Sn is a subring of R.](/uploads/image/z/946775-47-5.jpg?t=Let+R+be+an+arbitrary+ring+and+%EF%BC%88n%E5%B1%9E%E4%BA%8EZ%2B%EF%BC%89+.If+the+set+Sn+is+defined+bySn+%3D+%7B%EF%BC%88a+%E5%B1%9E%E4%BA%8E+R%EF%BC%89+l+%28n%5Ek%29+%2Aa+%3D+0+for+some+k+%3E+0%7Ddetermine+whether+Sn+is+a+subring+of+R.)
Let R be an arbitrary ring and (n属于Z+) .If the set Sn is defined bySn = {(a 属于 R) l (n^k) *a = 0 for some k > 0}determine whether Sn is a subring of R.
Let R be an arbitrary ring and (n属于Z+) .If the set Sn is defined by
Sn = {(a 属于 R) l (n^k) *a = 0 for some k > 0}
determine whether Sn is a subring of R.
Let R be an arbitrary ring and (n属于Z+) .If the set Sn is defined bySn = {(a 属于 R) l (n^k) *a = 0 for some k > 0}determine whether Sn is a subring of R.
答案:正确
∀a,b∈Sn,∃k1,k2>0,(n^k1) *a = 0,(n^k2)*b= 0,令k=max(k1,k2),则 (n^k) *a = 0,(n^k) *b= 0,于是(n^k) *(a-b)= 0,
故 a-b∈Sn,故Sn is a subring of R..
令R是任意一个环,且n属于Z+。如果Sn定义为:Sn = {(a 属于 R) l 对某个k > 0有 (n^k) *a = 0 },判断Sn是否是R上的一个子环。
这个结论是对的,您可以根据半环的定义去验证。
任意圆R(n属于Z+),假设Sn为确定值Sn = {(a 属于 R) l (n^k) *a = 0 时 k > 0},证明Sn是否是R的子圆。