A minimum depth is assigned to a ring homomorphism and a bimodule over its codomain. When the homomorphism is an inclusion and the bimodule is the codomain, the recent notion of depth of a subring in a paper by Boltje-Danz-Külshammer is recovered . Subring depth below an ideal gives a lower bound for BDK’s subring depth of a group algebra pair or a semisimple complex algebra pair.

The cohomology of operator algebras introduced by B. E. Johnson, R. V. Kadison, and J. R. Ringrose in a series of three papers is a useful tool for obtaining new invariants for operator algebras or to prove stability results by the vanishing of their cohomology groups (see [14]). If X is a von Neumann algebra and a Banach bimodule over M, and if « is a positive integer, then the nth cohomology ...

Motivated from some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define ...

We describe obstructions to a direct-limit preserving right-exact functor between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, all obstructions vanish and we recover Watts Theorem. We use our description of these obstructions to prove that if a direct-limit preserving right-exact functor F from a smooth curve is...