We introduce the notions of proto-complete, complete, complete⁎ and strong-complete objects in pointed categories. show under mild conditions on a exact protomodular category that every proto-complete (respectively complete) object is product an abelian object. This together with observation trivial group only complete recovers theorem Baer classifying groups. In addition we generalize several ...

in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

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For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...