Let F be a field and let E be an étale algebra over F , that is, a finite product of finite separable field extensions, E = F1 × · · · × Fr. The classical primitive element theorem asserts that if r = 1, then E is generated by one element as an F -algebra. The same is true for any r > 1, provided that F is infinite. However, if F is a finite field and r > 2, the primitive element theorem fails ...

We exhibit a separable commutative C*-algebra A such that A⊗K is homotopy equivalent to zero, without Mn(A) being so for any n ≥ 1.

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([17]) Ando-Kirchberg ([2]). In this paper we give a complete answer to their question: A C*-algebra has algebra if only satisfies Fell's condition. contrast, show that any non-trivial extension compact operators not non-abelian but even residually type I algebra. particular its...

Introduction. If one at tempts to make a systematic study of algebras with nonzero radical one soon realizes that the main difficulty is that of singling out a set of structural characteristics which could constitute a suitable center of interest in a general theory. In the study of simple and semisimple algebras, the full matrix algebras over the groundfield serve as models for the "perfect" s...