I must find an isomorphism between and .

The problem is that multiplication is defined entirely differently in the two rings. Any attempt by me to define an iso between the two breaks down at multiplication.

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- Nov 13th 2005, 04:29 PMTreadstone 71Isomorphism
I must find an isomorphism between and .

The problem is that multiplication is defined entirely differently in the two rings. Any attempt by me to define an iso between the two breaks down at multiplication. - Nov 13th 2005, 09:34 PMhpeQuote:

Originally Posted by**Treadstone 71**

**lift**the multiplication on to . For a different quadratic polynomial, you would get a different ring structure (a field for ). - Nov 14th 2005, 04:43 AMTreadstone 71
I'm not entirely sure what you mean by "lift" the multiplication. Isn't multiplication on Z5XZ5 defined as (a,b)(c,d)=(ac,bd)?

- Nov 14th 2005, 03:51 PMhpeQuote:

Originally Posted by**Treadstone 71**

Define by , where is the unique representative of degree less than 2 of an element in . This is a bijection. Then define

, where the multiplication on the right is the one in . Then work out what this means in . Compare this to the formula for complex multiplication, and think about an explanation.

Hope this helps.