To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

In this article, we will give a characterization of Banach bimodules over C∗-algebras of compact operators that arises from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a hyper-Stonian space. These two characterizations are concerned with whether certain natural map from a Banach bimodule to its canonical bidual is isometric (we call su...

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E ) over the linking groupoid L such that the full cross-sectional algebra of L(E ) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to groupoid crossed-products the fact, p...

We consider the problem of classifying all finite basis-transitive matroids and reduce it to the classification of the finite basis-transitive and point-primitive simple matroids (or geometric lattices, or dimensional linear spaces). Our main result shows how a basisand point-transitive simple matroid is decomposed into a so-called supersum. In particular each block of imprimitivity bears the s...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

The setup is as follows. We consider pairs (A,B) consisting of an A∞-algebra B and a subalgebra A. We will be primarily working with the category V = H0(mod(A)) of Amodules. However, that category inherits certain additional data from the presence of B. The most important such data are a functor F : V → V , given by tensor product with the quotient bimodule (B/A)[−1], together with a natural tr...

Given a finite dimensional algebra A of finite global dimension, we consider the trivial extension of A by the A − A-bimodule ⊕i≥2 Ext 2 A(DA,A), which we call the higher relation bimodule. We first give a recipe allowing to construct the quiver of this trivial extension in case A is a string algebra and then apply it to prove that, if A is gentle, then the tensor algebra of the higher relation...

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = ( T M D 0 U N 0 0 V )