Isomorphisms of endomorphism rings of rank one mixed groups

The endomorphism ring of a locally free module

“…(2) Uniqueness Problem: prove or disprove that any ring isomorphism of E R (M) onto E S (N) is induced by a semi-linear isomorphism of M R onto N s for all R, S £ 91 and M R , N s £ <31t. These problems are very difficult if 911 is allowed to be at all general, even for very restricted classes 91 [2,6,7,10,12,13,14,15,16,17,18,19,20,21,22,24]. In this paper, we restrict 9H to consist only of free or "almost free" modules, but we allow as much freedom as possible in the choice of 91.…”

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

“…For example (see [281] by Wolfson), for any cardinal number c there exist homogeneous completely decomposable groups G and H of rank c which are not isomorphic but have isomorphic rings of endomorphisms. For p-local Abelian groups see also [184] by May. In addition we give only a selective additional bibliography on endomorphism rings of Abelian groups: Bazzoni and Metelli [19], Dugas and Gobel [59], Gobel and May [99], Krylov [148], May [181,182,183,184], May and Toubassi [185,186,187,188,189], Metelli and Salce [197], Mikhalev [203], Puusemp [229], Sebeldin [239,238,240,241,242,243,244,248], Wolfson [279].…”