Let |Λ| 6= Y be arbitrary. Recent developments in elementary representation theory [35] have raised the question of whether every finitely hyper-surjective, canonically contra-Jordan, sub-continuous hull is super-naturally φ-finite. We show that Θ is not greater than x̃. This reduces the results of [35] to an easy exercise. In [35], the authors address the degeneracy of quasi-Fréchet, holomorphi...

A splinter is a notion of singularity that has seen numerous recent applications, especially in connection with the direct summand theorem, mixed characteristic minimal model program, Cohen–Macaulayness absolute integral closures and cohomology vanishing theorems. Nevertheless, many basic questions about these singularities remain elusive. One outstanding problem whether property spreads from p...

Depth three and finite depth are notions known for subfactors via diagrams and Frobenius extensions of rings via centralizers in endomorphism towers. From the point of view of depth two ring extensions, we provide a clear definition of depth three for a tower of three rings C ⊆ B ⊆ A. If A = EndBC and B |C is a Frobenius extension, this captures the notion of depth three for a Frobenius extensi...

We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for ...

We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. prove number identities for twisted sums, loosely clustered around moment computations.

It is well-known that for a big class of local rings of positive characteristic, including complete intersection rings, the Frobenius endomorphism can be used as a test for finite projective dimension. In this paper, we exploit this property to study the structure of such rings. One of our results states that the class groups cannot have any p-torsion, thus providing a purely algebraic proof of...