Semisimple corings

Details Semisimple corings Semisimple corings

2002-01-09

arxiv.org/abs/math/0201070v1

Mathematics

Rings and Algebras

Scientific paper

While semisimple artinian rings and semisimple coalgebras over a field can be described in terms of matrices (either matrix ring over division rings or comatrix coalgebras over the ground field), semisimple corings seem to have a more intrincated structure in general. It turns out that some well-known properties of semisimple rings or coalgebras, which are immediately deduced from the aforementioned structure, are not evident over a (left) semi-simple coring. For instance, it is not evident that the notion of semi-simple coring is left-right symmetric. To be precise, if every left comodule decomposes a a direct sum of simple comodules, do the right comodules have such a decomposition? In other words, is every left semi-simple coring a right semi-simple coring? We develope the basic essentials for a theory of semi-simple corings, giving a positive answer for the last question, as well as some information about the structure of semi-simple corings.

Affiliated with

Also associated with

No associations

Rating

Semisimple corings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Semisimple corings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semisimple corings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-124265