@MISC{Conrad_carlitzextensions, author = {Keith Conrad}, title = {CARLITZ EXTENSIONS}, year = {} }

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Abstract

The ring Z has many analogies with the ring Fp[T], where Fp is a field of prime size p. For example, for nonzero m ∈ Z and M ∈ Fp[T], the residue rings Z/(m) and Fp[T]/M are both finite. The unit groups Z × = {±1} and Fp[T] × = F × p are both finite. Every nonzero integer can be made positive after multiplication by a suitable sign ±1, and every