1. CMB Online first
|Jacobson Radicals of Skew Polynomial Rings of Derivation Type|
We provide necessary and sufficient conditions for a skew polynomial ring of derivation type to be semiprimitive, when the base ring has no nonzero nil ideals. This extends existing results on the Jacobson radical of skew polynomial rings of derivation type.
Keywords:skew polynomial rings, Jacobson radical, derivation
2. CMB 2012 (vol 57 pp. 80)
|Semicrossed Products of the Disk Algebra and the Jacobson Radical|
We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step, the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.
Keywords:semicrossed product, disk algebra, Jacobson radical
Categories:47L65, 47L20, 30J10, 30H50