On the dimension of the space of integrals on coalgebras
Dăscălescu, S. · Năstăsescu, C. · Toader, B.
Original · EN
We study the injective envelopes of the simple right C-comodules, and their duals, where C is a coalgebra. This is used to give a short proof and to extend a result of Iovanov on the dimension of the space of integrals on coalgebras. We show that if C is right co-Frobenius, then the dimension of the space of left M-integrals on C is ≤ dimM for any left C-comodule M of finite support, and the dimension of the space of right N-integrals on C is ≥ dimN for any right C-comodule N of finite support. If C is a coalgebra, it is discussed how far is the dual algebra C* from being semiperfect. Some examples of integrals are computed for incidence coalgebras.
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