Theses/Dissertations - Mathematics
Permanent URI for this collectionhttps://hdl.handle.net/2104/4791
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Browsing Theses/Dissertations - Mathematics by Subject "Chinese remainder theorem."
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Item On a ring associated to F[x].(2013-09-24) Aceves, Kelly Fouts.; Dugas, Manfred.; Mathematics.; Baylor University. Dept. of Mathematics.For a field F and the polynomial ring F [x] in a single indeterminate, we define Ḟ [x] = {α ∈ End_F(F [x]) : α(ƒ) ∈ ƒF [x] for all ƒ ∈ F [x]}. Then Ḟ [x] is naturally isomorphic to F [x] if and only if F is infinite. If F is finite, then Ḟ [x] has cardinality continuum. We study the ring Ḟ[x] for finite fields F. For the case that F is finite, we discuss many properties and the structure of Ḟ [x].