we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

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 show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...