Abstract
In the paper we describe, in terms of their generators, the prime and maximal ideals of a polynomial ring R[x] in one indeterminate over a principal ideal domain. We show how these results can be obtained by using only elementary abstract algebra. As examples we consider the rings Z[x], (Z the integers) D[x] (D a discrete valuation domain) and k[x, y] (k an algebraically closed field). Finally we show how the results can be used to illustrate several important results in commutative algebra.
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More From: International Journal of Mathematical Education in Science and Technology
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