I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2005, VOLUME 11, NUMBER 2, PAGES 51-72
Modules and comodules for corings
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A coring over
a ring is an -bimodule with
and a counit
both being left and right -linear mappings
satisfying additional conditions.
The dual spaces
allow the ring structure
and the right (left) comodules over can be considered as left
(right) modules over
In fact, under weak restrictions on the -module properties
of , the
category of right -comodules can be
identified with the subcategory
of -Mod, i.e., the
category subgenerated by the left -module .
This point of view allows one to apply results from module theory to
the investigation of coalgebras and comodules.
Last modified: June 9, 2005