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...

We give an example of a direct summand of a serial module that does not admit an indecomposable decomposition.

Given a sequence d→=(d1,…,dk) of natural numbers, we consider the Lie subalgebra h gl(d,F), where d=d1+⋯+dk and F is field characteristic 0, generated by two block upper triangular matrices D E partitioned according to d→, study problem computing nilpotency degree m nilradical n h. We obtain complete answer when belong certain family that arises naturally attempting classify indecomposable modu...