Frobenius extensions of QF-$3$ rings

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...

Extensions of Nilpotent P.P. Rings

Extensions of strongly alpha-reversible rings

We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...

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...

Are Biseparable Extensions Frobenius?

In Secion 1 we describe what is known of the extent to which a separable extension of unital associative rings is a Frobenius extension. A problem of this kind is suggested by asking if three algebraic axioms for finite Jones index subfactors are dependent. In Section 2 the problem in the title is formulated in terms of separable bimodules. In Section 3 we specialize the problem to ring extensi...