[代數] 結構
不好意思 想請問一下一些集合的結構
1. Z_9 x Z_6
2. Z_9 x Z_6 / <(3,3)>
( <(3,3)> be the cyclic subgroup of Z_9 x Z_6 generated by (3,3) )
以及下面這題
Consider the ringof Gassian integers Z[i]
(a) For a non-zero principal ideal J=<a+bi> in Z[i]
prove that Z[i]/J is a finite ring
(Hint: Z[i] is a Euclidean domain with norm v(x+yi)=x^2+y^2)
(b) What's the number of elements in Z[i]/J for J=<1+i>？
這題是97年台聯大考題 對於這方面的結構都不是挺了解
請多指點 感恩謝謝
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