In this paper, we prove that rational homogeneous bundles and log homogeneous varieties (studied by M. Brion) have an absolute Chow–Künneth decomposition. This strengthens the earlier paper by us on small dimensional varieties with a NEF tangent bundle, and using Hwang-Mok’s results, we get the results for new cases in higher dimension as well, for instance upto dimension four.

We show that every primary lattice can be considered a glueing of intervals having geometric dimension at least 3 and with a skeleton of breadth at most 2. We call this geometric decomposition. In the Arguesian case, we analyse the sub-glueings corresponding to cover preserving sublattices of the skeleton which are 2-element chains or a direct product of 2 such. We show that these admit a cover...

In an earlier paper a construction was given for an infinite-dimensional uniserial module over Q for SL(2,Z) whose composition factors are all isomorphic to the standard (two-dimensional) module. In this note we consider generalizations of this construction to other composition factors and to other rings of algebraic integers.

It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P , RP is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreove...

Let Λ be a commutative local uniserial ring of length n, p a generator of the maximal ideal, and k the radical factor field. The pairs (B, A) where B is a finitely generated Λ-module and A ⊆ B a submodule of B such that pmA = 0 form the objects in the category Sm(Λ). We show that in case m = 2 the categories Sm(Λ) are in fact quite similar to each other: If also ∆ is a commutative local uniseri...