Geodesic
Isomorphisms of the endomorphism semigroups op modules.~II
Algebra i logika, Tome 6 (1967) no. 2, pp. 35-47.

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In the present work we prove that if $R_1$ is an antimatrix ring (i.e . $R_1$ is not isomorphic to any matrix ring $S_n$, $n>1$, over a ring $S$) and if all projective modules over $R_2$ are free, then isomorphism $\Phi$ of multiplicative endomorphism semigroups of free modules is induced by a s.l.i. If $R_1$ and $R_2$ are ordered rings, $_{R_1}A_1$ and $_{R_2}A_2$ are free modules, $r(A_1)>1$, $D_1$ and $D_2$ are the multiplicative semigroups of all positive endomorphisms of the partially or­dered modules $A_1$ and $A_2$, $\Phi$ is an isomorphism of $D_1$ upon $D_2$ then $\Phi$ is induced by an orderly-semilinear isomorphism of $A_1$ upon $A_2$. 
@article{AL_1967_6_2_a3,
     author = {A. V. Mikhalev},
     title = {Isomorphisms of the endomorphism semigroups op {modules.~II}},
     journal = {Algebra i logika},
     pages = {35--47},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_1967_6_2_a3/}
}
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A. V. Mikhalev. Isomorphisms of the endomorphism semigroups op modules.~II. Algebra i logika, Tome 6 (1967) no. 2, pp. 35-47. http://geodesic.mathdoc.fr/item/AL_1967_6_2_a3/