Biring and plethory structures on integer-valued polynomial rings

Details Biring and plethory structures on integer-valued polynomial rings Biring and plethory structures on integer-valued polynomial rings

2011-09-18

arxiv.org/abs/1109.3848v1

Mathematics

Commutative Algebra

16 pages

Scientific paper

Let $A$ and $B$ be commutative rings with identity. An {\it $A$-$B$-biring} is an $A$-algebra $S$ together with the structure on $S$ of a $B$-algebra object in the opposite category of the category of $A$-algebras; equivalently, an $A$-$B$-biring 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 {\it $A$-plethory} is a monoid object in the monoidal category, equipped with the composition product, of $A$-$A$-birings. We show that $Int(D)$ has such a structure if $D = A$ is a domain such that the natural $D$-algebra homomorphism $\theta_n: {\bigotimes_D}_{i = 1}^n Int(D) \longrightarrow Int(D^n)$ is an isomorphism for $n = 2$ and injective for $n \leq 4$. This holds in particular if $\theta_n$ is an isomorphism for all $n$, which in turn holds, for example, if $D$ is a Krull domain or more generally a TV PVMD. In these cases we also examine properties of the functor $\Hom_D(Int(D),-)$ from $D$-algebras to $D$-algebras.

Affiliated with

Also associated with

No associations

Rating

Biring and plethory structures on integer-valued polynomial rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Biring and plethory structures on integer-valued polynomial rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biring and plethory structures on integer-valued polynomial rings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-560510