Let G = SpecA be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗ = R × B∗ as R-algebras and the first projection A∗ → R is the unit of A. If M is a dual functor of G-modules and wG := (1, 0) ∈ R×B ∗ =...

5. L. K. Hua, A note on the total matrix ring over a non-commutative field, Annales de la Société Polonaise de Mathématique vol. 25 (1952) pp. 188-198. 6. N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 479-502. 7. F. Kasch, Invariante Untermoduln des Endomorphismenrings eines Vektorraums, Archiv der Mathematik vol. 4 (1953) pp. 182-190. ...

We prove that two dual operator algebras are weak Morita equivalent in the sense of [4] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weakcontinuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case we can characterize such functors as the module normal Haagerup tensor product ...

The moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows are studied. It is actually shown that they are homeomorphic to those on dual modules associated with dual noncommutative flows. Moreover the method is also applicable to the case of noncommutative multi-flows.