In this paper we consider Artinian modules over power series rings endowed with a Frobenius map. We describe a method for finding the set of all prime annihilators of submodules which are preserved by the given Frobenius map and on which the Frobenius map is not nilpotent. This extends the algorithm by Karl Schwede and the first author, which solved this problem for submodules of the injective ...

1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Definition of the Witt Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Proof of the Existence of the Witt Rings . . . . . . . . ....

We study co-Frobenius and more generally Quasi-co-Frobenius corings over arbitrary baserings and over PF baserings in particular. We generalize some results about (Quasi-) co-Frobenius coalgebras to the case of non-commutative base rings and give several new characterisations for co-Frobenius and Quasi-co-Frobenius corings, some of them are new even in the coalgebra situation. We construct Mori...

We introduce a notion of depth three tower of three rings C ⊆ B ⊆ A with depth two ring extension A |B recovered when B = C. If A = EndBC and B |C is a Frobenius extension, this captures the notion of depth three for a Frobenius extension in [12, 13] such that if B |C is depth three, then A |C is depth two (a phenomenon of finite depth subfactors, see [20]). We provide a similar definition of f...

We introduce fusion bialgebras and their duals systematically study Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of rings. prove Hausdorff-Young inequality, uncertainty principles for duals. show that Schur product property, Young's inequality sum-set estimate hold bialgebras, but not always If ring is Grothendieck a catego...