The ring of Laurent polynomials F [ t, t - 1 ] over a field F is much like the p

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The ring of Laurent polynomials F [ t, t - 1 ] over a field F is much like the polynomial ring, but we allow negative powers of t as well as positive. Thus F [ t, t - 1 ] is the set of all formal sums where only finitely many a, are nonzero. The rules of addition and multiplication are just extensions of the addition and multiplication of polynomials: and where ck, the coefficient of tk, is defined to be Verify that F [ t, t - 1 ] is a ring. Show that there are no zerodivisors in F [ t, t - 1 ] , so it is an integral domain. Show that uF [ t, t - 1 ] consists of the elements ati, where a F, a 0.

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