Mersenne banner

Actes des rencontres du CIRM

Feuilleter
ou
  • Tout
  • Auteur
  • Titre
  • Bibliographie
  • Plein texte
NOT
Entre et
  • Tout
  • Auteur
  • Titre
  • Date
  • Bibliographie
  • Plein texte
  • Précédent
  • Feuilleter
  • Tome 2 (2010)
  • no. 2
  • p. 53-58
  • Suivant
no. 2

Birings and plethories of integer-valued polynomials
Jesse Elliott
Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 53-58.
  • Résumé

Let A and B be commutative rings with identity. 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 A-plethory is a monoid object in the monoidal category, equipped with the composition product, of A-A-birings. The polynomial ring A[X] is an initial object in the category of such structures. The D-algebra Int(D) has such a structure if D=A is a domain such that the natural D-algebra homomorphism θ n :⨂ D i=1 n Int(D)→Int(D n ) is an isomorphism for n=2 and injective for n≤4. This holds in particular if θ 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, which we hope to show is a new object worthy of investigation in the theory of integer-valued polynomials.

  • Détail
  • BibTeX
  • Comment citer
Publié le : 2011-10-20
DOI : https://doi.org/10.5802/acirm.34
Classification : 13G05,  13F20,  13F05,  16W99
Mots clés : Biring, plethory, integer-valued polynomial.
@article{ACIRM_2010__2_2_53_0,
     author = {Jesse Elliott},
     title = {Birings and plethories of integer-valued polynomials},
     journal = {Actes des rencontres du CIRM},
     pages = {53--58},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.5802/acirm.34},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.34/}
}
Elliott, Jesse. Birings and plethories of integer-valued polynomials. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 53-58. doi : 10.5802/acirm.34. https://acirm.centre-mersenne.org/articles/10.5802/acirm.34/
  • Bibliographie

[1] G. Bergman and A. Hausknecht, Cogroups and Co-Rings in Categories of Associative Rings, Mathematical Surveys and Monographs, Volume 45, American Mathematical Society, 1996.

[2] J. Borger and B. Wieland, Plethystic algebra, Adv. Math. 194 (2005) 246–283.

[3] P.-J. Cahen and J.-L. Chabert, Integer-Valued Polynomials, Mathematical Surveys and Monographs, vol. 48, American Mathematical Society, 1997.

[4] J. Elliott, Binomial rings, integer-valued polynomials, and λ-rings, J. Pure Appl. Alg. 207 (2006) 165–185.

[5] J. Elliott, Universal properties of integer-valued polynomial rings, J. Algebra 318 (2007) 68–92.

[6] J. Elliott, Some new approaches to integer-valued polynomial rings, in Commutative Algebra and its Applications: Proceedings of the Fifth Interational Fez Conference on Commutative Algebra and Applications, Eds. Fontana, Kabbaj, Olberding, and Swanson, de Gruyter, New York, 2009.

[7] J. Elliott, Biring and plethory structures on integer-valued polynomial rings, to be submitted for publication.

[8] C. J. Hwang and G. W. Chang, Bull. Korean Math. Soc. 35 (2) (1998) 259–268.

[9] D. O. Tall and G. C. Wraith, Representable functors and operations on rings, Proc. London Math Soc. (3) 20 (1970) 619–643.

Diffusé par : Publié par : Développé par :
  • Nous suivre
e-ISSN : 2105-0597
© 2009 - 2021 Centre Mersenne, Actes des rencontres du CIRM, et les auteurs