Rings of Frobenius operators

Rings of Frobenius operators

Let R be a local ring of prime characteristic. We study the ring of Frobenius operators F(E), where E is the injective hull of the residue field of R. In particular, we examine the finite generation of F(E) over its degree zero component F0(E), and show that F(E) need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of F(E) in good generalit...

Weighted Frobenius-Perron and Koopman operators

Reducible Reversibility for Frobenius Rings

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...

FTF Rings and Frobenius Extensions

The notion of FTF ring (see Definition 1.1 or Proposition 1.2) captures homological and finiteness properties shared by several classes of rings. Thus coherent rings with left flat-dominant dimension ≥ 1 [3, Corolario 2.2.11] or rings having quasi-Frobenius two-sided maximal quotient ring [7, Proposition 3.6; 3, Teorema 2.3.10] are examples of FTF rings. Moreover, FTF ring and QF-3 ring are rel...

Multiple Perron-Frobenius operators.

A cycle expansion technique for discrete sums of several PF operators, similar to the one used in the standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particular mappings entering the sum.