The model theory of metric structures ([?]) was successfully applied to analyze ultrapowers of C*-algebras in [?] and [?]. Since important classes of separable C*-algebras, such as UHF, AF, or nuclear algebras, are not elementary (i.e., not characterized by their theory—see [?, §6.1]), for a moment it seemed that model theoretic methods do not apply to these classes of C*-algebras. We prove res...

Let φ be a linear-fractional self-map of the open unit disk D, not an automorphism, such that φ(ζ) = η for two distinct points ζ, η in the unit circle ∂D. We consider the question of which composition operators lie in C∗(Cφ,K), the unital C∗-algebra generated by the composition operator Cφ and the ideal K of compact operators, acting on the Hardy space H.

Recall that a rng is a ring which is possibly non-unital. In this note, we address the problem whether every finitely generated idempotent rng (abbreviated as irng) is singly generated as an ideal. It is well-known that it is the case for a commutative irng. We prove here it is also the case for a free rng on finitely many idempotents and for a finite irng. A relation to the Wiegold problem for...

In 1982 Richard P. Stanley conjectured that any finitely generated Zn-graded module M over a finitely generated Nn-graded K-algebra R can be decomposed as a direct sum M = ⊕t i=1 νi Si of finitely many free modules νi Si which have to satisfy some additional conditions. Besides homogeneity conditions the most important restriction is that the Si have to be subalgebras of R of dimension at least...

We give an explicit description of the tracial state simplex C ⁎ -algebra ( G ) arbitrary connected, second countable, locally compact, solvable group . show that every lifts from a abelianized group, and intersection kernels all states is proper ideal unless abelian. As consequence, connected nonabelian Lie cannot embed into simple unital AF-algebra.

Using different descriptions of the Cuntz semigroup and Pedersen ideal, it is shown that $\sigma$-unital simple $C^*$-algebras with almost unperforated semigroup, a unique lower semicontinuous $2$-quasitrace whose stabilization has stable rank $1$ are either or algebraically simple.

1. Introduction. When studying ideal theory in semirings, it is natural to consider the quotient structure of a semiring modulo an ideal. If 7 is an ideal in a semiring R, the collection {x+l}xeit oí sets x + I={x+i\iEl} need not be a partition of R. Faced with this problem, [2] used equivalence relations to determine cosets relative to an ideal. La Torre successfully established analogues of s...

it is shown that every  almost linear bijection $h : arightarrow b$ of a unital $c^*$-algebra $a$ onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in a$, all $y in a$, and all $nin mathbb z$, andthat almost linear continuous bijection $h : a rightarrow b$ of aunital $c^*$-algebra $a$ of real rank zero onto a unital$c^*$-algebra...

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogeneuous ideals of R(M) have the form I(+)N where I is an ideal of R, N a submodule of M such that IM ⊆ N . In particular, [N : M ] (+)N is a homogeneous ideal of R(M). The purpose of this paper is to investigate how properties of the ideal [N : M ](+)N are re...