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This article is cited in 2 scientific papers (total in 2 papers)
Isomorphisms of the endomorphism semigroups op modules. II
A. V. Mikhalev
Abstract:
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 $A_2$.
Received: 24.01.1967
Citation:
A. V. Mikhalev, “Isomorphisms of the endomorphism semigroups op modules. II”, Algebra i Logika. Sem., 6:2 (1967), 35–47
Linking options:
https://www.mathnet.ru/eng/al1094 https://www.mathnet.ru/eng/al/v6/i2/p35
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Abstract page: | 93 | Full-text PDF : | 27 |
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