Galois comodules
| dc.creator | Brzezinski, Tomasz | |
| dc.date | 2003-12-08 | |
| dc.date | 2004-04-28 | |
| dc.date.accessioned | 2026-07-07T05:03:39Z | |
| dc.date.available | 2026-07-07T05:03:39Z | |
| dc.description | Galois comodules of a coring are studied. The conditions for a simple comodule to be a Galois comodule are found. A special class of Galois comodules termed principal comodules is introduced. These are defined as Galois comodules that are projective over their comodule endomorphism rings. A complete description of principal comodules in the case a background ring is a field is found. In particular it is shown that a (finitely generated and projective) right comodule of an $A$-coring $\mathcal C$ is principal provided a lifting of the canonical map is a split epimorphism in the category of left $\mathcal C$-comodules. This description is then used to characterise principal extensions or non-commutative principal bundles. Specifically, it is proven that, over a field, any entwining structure consisting of an algebra $A$, a coseparable coalgebra $C$ and a bijective entwining map $ψ$ together with a group-like element in $C$ give rise to a principal extension provided the lifted canonical map is surjective. Induction of Galois and principal comodules via morphisms of corings is described. A connection between the relative injectivity of a Galois comodule and the properties of the extension of endomorphism rings associated to this comodule is revealed. | |
| dc.description | 36 pages, LaTeX; a few corrections to version 2 | |
| dc.identifier | https://arxiv.org/abs/math/0312159 | |
| dc.identifier | http://arxiv.org/abs/math/0312159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69508 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W30; 13B02 | |
| dc.title | Galois comodules | |
| dc.type | text |