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Post Closed as "Not suitable for this site" by Stefan Kohl♦, Henry.L, Michael Albanese, user6976, Yoav Kallus
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Ricardo Andrade
Ricardo Andrade
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Can I define the polynomial ring A[x] with an isomorphism f: A ---> A[x]  ?

Hi, I'm sorry if this isn't an appropriate question for MO. I've been reading here for a while, but I still haven't got a good grasp of what's a good question.

Given a field A and the polynomial ring A[x], we order the elements of A in any sequence and we define the isomorphism $f\colon A\to A[x]$ such that every element an$\mapsto$an xn, an $\in$ A, xn $\in$ A[x].

Can this be considered an alternate definition for A[x], is it just wrong, or is it the same as the canonical one?

Andy

Can I define the polynomial ring A[x] with an isomorphism f: A ---> A[x]  ?

Hi, I'm sorry if this isn't an appropriate question for MO. I've been reading here for a while, but I still haven't got a good grasp of what's a good question.

Given a field A and the polynomial ring A[x], we order the elements of A in any sequence and we define the isomorphism $f\colon A\to A[x]$ such that every element an$\mapsto$an xn, an $\in$ A, xn $\in$ A[x].

Can this be considered an alternate definition for A[x], is it just wrong, or is it the same as the canonical one?

Andy

Can I define the polynomial ring A[x] with an isomorphism f: A ---> A[x]?

I'm sorry if this isn't an appropriate question for MO. I've been reading here for a while, but I still haven't got a good grasp of what's a good question.

Given a field A and the polynomial ring A[x], we order the elements of A in any sequence and we define the isomorphism $f\colon A\to A[x]$ such that every element an$\mapsto$an xn, an $\in$ A, xn $\in$ A[x].

Can this be considered an alternate definition for A[x], is it just wrong, or is it the same as the canonical one?

Andy

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Andy Lana
Andy Lana
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Can I define the polynomial ring A[x] with an isomorphism f: A ---> A[x] ?

Hi, I'm sorry if this isn't an appropriate question for MO. I've been reading here for a while, but I still haven't got a good grasp of what's a good question.

Given a field A and the polynomial ring A[x], we order the elements of A in any sequence and we define the isomorphism $f\colon A\to A[x]$ such that every element an$\mapsto$an xn, an $\in$ A, xn $\in$ A[x].

Can this be considered an alternate definition for A[x], is it just wrong, or is it the same as the canonical one?

Andy