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 $L$; $alpha in L[X]$ a monic irreducible polynomial; $xi$ any root of $alpha$ in $F$; and $Q=langle P,alpha angle$, the upper to $P$ with respect to $alpha$. Then $R[X]/Q$ is $R$-algebra isomorphic to $D[xi ]$; and is $R$-isomorphic to an overring of $D$ if and only if $deg(alpha )=1$.

Keywords: Commutative ring, prime ideal, polynomial ring, upper, integral domain, factor ring, degree