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Let $A$ and $B$ be commutative rings with identity. An is an $A$-algebra $S$ together with a lift of the functor ${Hom}_A(S,-)$ from $A$-algebras to sets to a functor from $A$-algebras to $B$-algebras. An is a monoid object in the monoidal category, equipped with the composition product, of $A$-$A$-birings. The polynomial ring $A\left[X\right]$ is an initial object in the category of such structures. The $D$-algebra $Int\left(D\right)$ has such a structure if $D=A$ is a domain such that the natural $D$-algebra homomorphism ${\theta }_n:{{⨂}_D}_{i=1}^{n}Int\left(D\right)\to Int\left(D^n\right)$ is an isomorphism for $n=2$ and injective for...