… modules over a semi-simple ring. As a generalization of isomorphisms between modules
over a ring we have the notion of semi-linear isomorphisms. But even this notion is not general …

… isomorphisms of endomorphism semigroups of modules. We touch some related topics. First
of all, we describe recent results on isomorphisms … determined by their module category. In …

… Since the identity map on a ring is clearly an isomorphism from the ring to itself, we have
as an easy application of (1.1) that the relation of "being isomorphic" satisfies the usual …

… For example, Morita's theorem characterizing the similarity of two rings A and B, that is, …
module P which generates the category mod-B, and for which there is a ring isomorphism A≈ …

… is the category of GE MR such that eG is an isomorphism, (… ring R by letting module refer to
right R-module. Thus G and G' denote (right R-)modules, MR denotes the category of modules…

… In this way, we obtain an isomorphism of categories between MR and M̂R . In general, there
exists no unital ring S such that MR is isomorphic to MS, even if R is firm. However, we can …

… in which such a uniqueness up to isomorphism of direct-sum … rings and modules with a
semilocal endomorphism ring. If R is a semilocal ring and MR is a finitely presented module, then …

… one considers modules over the completed group ring A=Zp[[… to quasiisomorphism, ie, by
neglecting finite G-modules. In … the category of pseudo-compact A-modules and the category of …

… ring of a module which is the direct sum of more than three isomorphic submodules is determined
up to isomorphism by … For a ring R we denote the category of all left R-modules by -PR …

… Since the identity map on a ring is clearly an isomorphism from the ring to itself, we have
as an easy application of (1.1) that the relation of “being isomorphic” satisfies the usual …