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Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P ; L the quotient field of D; F an algebraic closure of L; α ∈ L[X] a monic irreducible polynomial; ξ any root of α in F ; and Q = P, α , the upper to P with respect to α. Then R[X]/Q is R-algebra isomorphic to D[ξ]; and is R-isomorphic to an overring of D if and only if deg(α) = 1.doi:10.5666/kmj.2010.50.1.001 fatcat:lbem72rnivckha3smhbtk5pdby