Idempotent plethories

JOURNAL OF ALGEBRA

卷:463

Article

关键词: Commutative ring;    Biring;    Biring triple;    Plethory;    Tall-Wraith monad;    Monad;    Comonad;    Triple;    Eilenberg-Moore category;    Integral domain;    Integer-valued polynomial;    Binomial ring;    Dedekind domain;    Krull domain;   

DOI  :  10.1016/j.jalgebra.2016.06.008

来源: Elsevier

【 摘 要 】

Let k be a commutative ring with identity. A k-plethory is a commutative k-algebra P together with a comonad structure Wp, called the P-Witt ring functor, on the covariant functor that it represents. We say that a k-plethory P is idempotent if the comonad Wp is idempotent, or equivalently if the map from the trivial k-plethory k[e] to P is a k-plethory epimorphism. We prove several results on idempotent plethories. We also study the k-plethories contained in K[e], where K is the total quotient ring of k, which are necessarily idempotent and contained in Int(k) = (f is an element of K[e] : f(k) subset of k}. For example, for any ring 1 between k and K we find necessary and sufficient conditions all of which hold if k is a integral domain of Krull type so that the ring Int(i)(k) = Int(k) boolean AND l[e] has the structure, necessarily unique and idempotent, of a k-plethory with unit given by the inclusion k[e] Int/ (k). Our results, when applied to the binomial plethory Int(Z), specialize to known results on binomial rings. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free