Change of base for operator space modules

We prove a change of base theorem for operator space modules over C*-algebras, analogous to the change of rings for algebraic modules. We demonstrate how this can be used to show that the category of (right) matrix normed modules and completely bounded module maps has enough injectives.

Euler characteristic on noncommutative polyballs

In this paper we introduce and study the Euler characteristic (denoted by χ) associated with algebraic modules generated by arbitrary elements of certain noncommutative polyballs. We provide several asymptotic formulas for χ and prove some of its basic properties. We show that the Euler characteristic is a complete unitary invariant for the finite rank Beurling type invariant subspaces of the tensor product of full Fock spaces

Stable Lattices

The most interesting cases of stable lattices, introduced in an earlier volume of this journal (12), were the (algebraic) modules of stable norm, or modules whose ratio of minimum absolute non-zero norm to lattice determinant (i.e., to the square root of module-discriminant) is a local maximum for small variations of the basis. We soon found that these modules were perhaps more numerous than we should have desired if we were interested only in finding an absolute maximum.