caa a22 4500 467882703 CHVBK 20180406152724.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10485-006-9044-5 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9044-5 The Galois Theory of Matrix C -rings [Elektronische Daten] [Tomasz Brzeziński, Ryan Turner] 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. Springer Science + Business Media B.V., 2006 C -ring nationallicence matrix ring context nationallicence Galois module nationallicence bicomodule nationallicence coalgebra nationallicence Brzeziński Tomasz Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK aut Turner Ryan Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK aut Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 471-501 0927-2852 14:5-6<471 2006 14 10485 https://doi.org/10.1007/s10485-006-9044-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9044-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brzeziński Tomasz Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK aut NATIONALLICENCE 700 1- Turner Ryan Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 471-501 0927-2852 14:5-6<471 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer