Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493138 | Journal of Algebra | 2005 | 35 Pages |
Abstract
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 C is principal provided a lifting of the canonical map is a split epimorphism in the category of left 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 Ï 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Tomasz BrzeziÅski,