Abstract We construct two types of unital separable simple $C^*$ -algebras: $A_z^{C_1}$ and $A_z^{C_2}$ , one exact but not amenable, the other nonexact. Both have same Elliott invariant as Jiang–Su algebra – namely, $A_z^{C_i}$ has a unique tracial state, $$ \begin{align*} \left(K_0\left(A_z^{C_i}\right), K_0\left(A_z^{C_i}\right)_+, \left[1_{A_z^{C_i}} \right]\right)=(\mathbb{Z}, \mathbb{Z}_+...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

Quasi-abelian categories are abundant in functional analysis and representation theory. It is known that a quasi-abelian category $\mathcal{E}$ cotilting torsionfree class of an abelian category. In fact, this property characterizes categories. This ambient derived equivalent to the $\mathcal{E}$, can be constructed as heart $\mathcal{LH}(\mathcal{E})$ $t$-structure on bounded $\mathbf{D}^b(\ma...

We characterize the categories with finite limits whose exact completions are toposes. We review the examples in the literature and also find new examples and counterexamples.

The notion of an internal category in a left exact cosimplicial category is introduced. For any topos over sets a certain left exact cosimplicial category is constructed functorially and the category of internal categories in it is investigated. The notion of a fundamental group is defined for toposes admitting the notion of “a discrete category.” Introduction Our primary interest in this paper...