FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 2, PAGES 51-72

Modules and comodules for corings

R. Wisbauer

Abstract

View as HTML     View as gif image

A coring $C$ over a ring $A$ is an $(A,A)$-bimodule with a comultiplication $$D: C → C Ä_A C and a counit $$e: C → A, both being left and right $A$-linear mappings satisfying additional conditions. The dual spaces $C*=\; Hom$_A(C,A) and $*C\; =$_AHom(C,A) allow the ring structure and the right (left) comodules over $C$ can be considered as left (right) modules over $$*C (respectively, $C$*). In fact, under weak restrictions on the $A$-module properties of $C$, the category of right $C$-comodules can be identified with the subcategory $$s[_^*CC] of $$*C-Mod, i.e., the category subgenerated by the left $$*C-module $C$. This point of view allows one to apply results from module theory to the investigation of coalgebras and comodules.

Location: http://mech.math.msu.su/~fpm/eng/k05/k052/k05204h.htm
Last modified: June 9, 2005