Let R be an arbitrary ring and (n属于Z+) .If the set Sn is def

topalpha2022-10-04 11:39:543条回答

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.

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shelly1130 共回答了20个问题 | 采纳率100%
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..
1年前
pa8pt 共回答了7个问题 | 采纳率
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。
1年前
紫藤隐雪 共回答了20个问题 | 采纳率75%
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。
1年前

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