Flexible partially stable algebras

Partially Ordered Pattern Algebras

A partial order on a set A induces a partition of each power An into “patterns” in a natural way. An operation on A is called a -pattern operation if its restriction to each pattern is a projection. We examine functional completeness of algebras with -pattern fundamental operations.

On Partially Additive Kleene Algebras

We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing algebraic structures, by exhibiting categorical connections with Kleene algebras, partially additiv...

Flexible Nilstable Algebras

On Flexible Quadratic Algebras

Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.

Z-stable Ash Algebras

The Jiang–Su algebra Z has come to prominence in the classification program for nuclear C-algebras of late, due primarily to the fact that Elliott’s classification conjecture predicts that all simple, separable, and nuclear C-algebras with unperforated K-theory will absorb Z tensorially (i.e., will be Z-stable). There exist counterexamples which suggest that the conjecture will only hold for si...