Add to ORKGLet C be a locally finitely presented additive category, and let E be a finitely presented pure-injective object of C. We prove that E has an indecomposable decomposition if and only if every pure epimorphic image of E is pure-injective if and only if the endomorphism ring of E is semiperfect. This extends a module-theoretic result which generalises the classical Osofsky Theorem
It is proven each ring $R$ for which every indecomposable right module is pure-projective is right p...
It is proven each ring $R$ for which every indecomposable right module is pure-projective is right p...
AbstractPure morphisms in locally presentable categories were characterized as directed colimits of ...
AbstractWe give a criterion for the existence of an indecomposable decomposition of pure-injective o...
In this note, we prove that if A is a finitely accessible additive category, then for every object A...
AbstractWe give a criterion for the existence of an indecomposable decomposition of pure-injective o...
For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcatgory of...
Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$...
Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$...
Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$...
It is proved that if A is an object in a finitely accessible additive category A such that A has fin...
AbstractA uniqeness result for direct sum decompositions into uniform objects is proved. The result ...
AbstractWe study copure semisimple Grothendieck categories, i.e. Krull–Schmidt categories satisfying...
AbstractFor a left pure semisimple ring R, it is shown that the local duality establishes a bijectio...
We show that in a finitely accessible additive category every class of objects closed under direct l...
It is proven each ring $R$ for which every indecomposable right module is pure-projective is right p...
It is proven each ring $R$ for which every indecomposable right module is pure-projective is right p...
AbstractPure morphisms in locally presentable categories were characterized as directed colimits of ...
AbstractWe give a criterion for the existence of an indecomposable decomposition of pure-injective o...
In this note, we prove that if A is a finitely accessible additive category, then for every object A...
AbstractWe give a criterion for the existence of an indecomposable decomposition of pure-injective o...
For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcatgory of...
Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$...
Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$...
Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$...
It is proved that if A is an object in a finitely accessible additive category A such that A has fin...
AbstractA uniqeness result for direct sum decompositions into uniform objects is proved. The result ...
AbstractWe study copure semisimple Grothendieck categories, i.e. Krull–Schmidt categories satisfying...
AbstractFor a left pure semisimple ring R, it is shown that the local duality establishes a bijectio...
We show that in a finitely accessible additive category every class of objects closed under direct l...
It is proven each ring $R$ for which every indecomposable right module is pure-projective is right p...
It is proven each ring $R$ for which every indecomposable right module is pure-projective is right p...
AbstractPure morphisms in locally presentable categories were characterized as directed colimits of ...