Depth Two, Normality, and a Trace Ideal Condition for Frobenius Extensions

Subring Depth, Frobenius Extensions, and Towers

The minimum depth d B,A of a subring B ⊆ A introduced in the work of Boltje, Danz and Külshammer 2011 is studied and compared with the tower depth of a Frobenius extension. We show that d B,A < ∞ if A is a finite-dimensional algebra and B has finite representation type. Some conditions in terms of depth and QF property are given that ensure that the modular function of a Hopf algebra restricts ...

A sufficient normality condition for Turing's formula

Normality: A Consistency Condition for Concurrent Objects

Linearizability is a consistency condition for concurrent objects (objects shared by concurrent processes) that exploits the semantics of abstract data types. It provides the illusion that each operation applied by concurrent processes takes eeect instantaneously at some point between the beginning and the end of its execution. When compared with other consistency conditions (such as sequential...

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...

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...