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Let $(X_\alpha)_{\alpha <\kappa}$ be an inverse system of abelian groups. If $\kappa = \omega$ (or by extension if $\kappa$ is of countable cofinality), then the Mittag-Leffler condition is a ...

In category of abelian groups, we know that — values of $\rm{lim}^1$ on countable systems are precisely cotorsion groups — values of $\rm{lim}^1$ on systems of finitely generated groups are of the ...

Let $A$ be a local domain. We let $T=T(A) $ be the subgroup of $\mathrm{SL}_{2}$ consisting of diagonal matrices and $V$ be the subgroup of unital matrices of $\mathrm{SL}_{2}$; i.e. $V:=\left\{\left( ...