A category of matrices representing two categories of Abelian groups

Invariants for abelian groups and dual exact sequences

“…It has been shown in [18] that A 0 is a finitely presented Z -module and the elements a . That is f (a r ) = t r1 b 1 + · · · + t rk b k = k s=1 t rs b s for 1 r n. As it is mentioned above, the homomorphism …”

“…Moreover, taking into account the fact that every finitely presented Z -module M can be presented in the form M ∼ = Hom( A/F A , Q /Z ) for some torsion free group A, see [18], we can deduce from (7) the isomorphism M ∼ = Hom(Hom Z (M, Q /Z ), Q /Z ). Analogously identifying along it, we obtain the equality M = Hom Hom…”

“…. , a n form a basis of the quotient divisible group A, see [18][19][20]. The functor S → D maps the object x 1 , .…”

“…The homomorphisms of the first row in the diagram (18) are the restrictions of the homomorphisms j * and i * . The equalities (20) show in particular that this row is exact.…”

“…We begin with the result obtained in [18]. The three categories and three pairs of mutually inverse functors between them form the following commutative diagram:…”