On invertibility preserving linear mappings, simultaneous triangularization and Property L Original Research Article

Let image be a unital matrix algebra, image a unital linear mapping and image the algebra generated by image . The mapping phi is a homomorphism modulo the Jacobson radical in image if and only if for image the mapping image preserves invertibility. This result is closely related to the question on the relationship between Property L and simultaneous triangularization. We introduce a Property kL and give criteria in terms of conditions on matrix pencils with coefficients in image rather than in image which ensure simultaneous triangularization.