Let R be a left pure semisimple ring such that there are no nonzero homomorphisms from preinjective modules to non-preinjective indecomposable modules in R-mod, and let W be the left key R-module; i.e., W is the direct sum of all non-isomorphic non-preinjective indecomposable direct summands of products of preinjective left R-modules. We show that if the module W is endofinite, then R is a ring...

Abstract The aim of the paper is to generalize decomposition theorems showed in Bagheri-Bardi et al. (Linear Algebra Appl 583:102–118, 2019; Linear 539:117–133, 2018) by a unified approach. We show general theorem with respect hereditary property. Then vast majority decompositions known algebra Hilbert space operators generalized elements Baer $$*$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

We use Quillen model structures to show a systematic method lift recollements of hereditary abelian categories their associated homotopy categories. To that end, we the notion adjoint triples and investigate transfers along pairs. Applications include liftings module derived counterpart, provide models for stable Gorenstein projective injective modules n-morphism over Iwanaga-Gorenstein rings.

We relate the endomorphism rings of certain D-elliptic sheaves of finite characteristic to hereditary orders in central division algebras over function fields.