NDLI: The Galois Theory of Matrix C-rings

Content Provider	Springer Nature Link
Author	Brzeziński, Tomasz Turner, Ryan B.
Copyright Year	2006
Abstract	A theory of monoids in the category of bicomodules of a coalgebra C or C-rings is developed. This can be viewed as a dual version of the coring theory. The notion of a matrix ring context consisting of two bicomodules and two maps is introduced and the corresponding example of a C-ring (termed a matrix C -ring) is constructed. It is shown that a matrix ring context can be associated to any bicomodule which is a one-sided quasi-finite injector. Based on this, the notion of a Galois module is introduced and the structure theorem, generalising Schneider’s Theorem II [Schneider, Isr. J. Math., 72:167–195, 1990], is proven. This is then applied to the C-ring associated to a weak entwining structure and a structure theorem for a weak A-Galois coextension is derived. The theory of matrix ring contexts for a firm coalgebra (or infinite matrix ring contexts) is outlined. A Galois connection associated to a matrix C-ring is constructed.
Ending Page	501
Page Count	31
Starting Page	471
File Format	PDF
ISSN	09272852
e-ISSN	15729095
Journal	Applied Categorical Structures
Issue Number	5-6
Volume Number	14
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-11-16
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Galois module coalgebra Geometry Convex and Discrete Geometry Theory of Computation matrix ring context bicomodule C-ring Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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