Duality and rational modules in Hopf algebras over commutative rings

J. Y. Abuhlail; J. Gómez-Torrecillas; F. J. Lobillo

doi:10.1006/jabr.2001.8722

Duality and rational modules in Hopf algebras over commutative rings

J. Y. Abuhlail^*
, J. Gómez-Torrecillas
, F. J. Lobillo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Let A be an algebra over a commutative ring R. If R is noetherian and A° is pure in R^A, then the categories of rational left A-modules and right A°-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner-Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A° in R^A.

Original language	English
Pages (from-to)	165-184
Number of pages	20
Journal	Journal of Algebra
Volume	240
Issue number	1
DOIs	https://doi.org/10.1006/jabr.2001.8722
State	Published - 1 Jun 2001
Externally published	Yes

Keywords

Comodule
Duality
Rational module

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1006/jabr.2001.8722

Cite this

@article{1c344810b5004d86ac992b9edf723ec0,

title = "Duality and rational modules in Hopf algebras over commutative rings",

abstract = "Let A be an algebra over a commutative ring R. If R is noetherian and A° is pure in RA, then the categories of rational left A-modules and right A°-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner-Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A° in RA.",

keywords = "Comodule, Duality, Rational module",

author = "Abuhlail, \{J. Y.\} and J. G{\'o}mez-Torrecillas and Lobillo, \{F. J.\}",

year = "2001",

month = jun,

day = "1",

doi = "10.1006/jabr.2001.8722",

language = "English",

volume = "240",

pages = "165--184",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Duality and rational modules in Hopf algebras over commutative rings

AU - Abuhlail, J. Y.

AU - Gómez-Torrecillas, J.

AU - Lobillo, F. J.

PY - 2001/6/1

Y1 - 2001/6/1

N2 - Let A be an algebra over a commutative ring R. If R is noetherian and A° is pure in RA, then the categories of rational left A-modules and right A°-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner-Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A° in RA.

AB - Let A be an algebra over a commutative ring R. If R is noetherian and A° is pure in RA, then the categories of rational left A-modules and right A°-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner-Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A° in RA.

KW - Comodule

KW - Duality

KW - Rational module

UR - https://www.scopus.com/pages/publications/0035374276

U2 - 10.1006/jabr.2001.8722

DO - 10.1006/jabr.2001.8722

M3 - Article

AN - SCOPUS:0035374276

SN - 0021-8693

VL - 240

SP - 165

EP - 184

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Duality and rational modules in Hopf algebras over commutative rings

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this