FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

**Modules and comodules for corings**

R.
Wisbauer

Abstract

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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 $*C\; =$_{A}Hom(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[_{*C}C]
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