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Algebra i Logika. Seminar, 1967, Volume 6, Number 2, Pages 35–47 (Mi al1094)  

This article is cited in 2 scientific papers (total in 2 papers)

Isomorphisms of the endomorphism semigroups op modules. II

A. V. Mikhalev
Full-text PDF (430 kB) Citations (2)
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
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Mikhalev, “Isomorphisms of the endomorphism semigroups op modules. II”, Algebra i Logika. Sem., 6:2 (1967), 35–47
Citation in format AMSBIB
\Bibitem{Mik67}
\by A.~V.~Mikhalev
\paper Isomorphisms of the endomorphism semigroups op modules.~II
\jour Algebra i Logika. Sem.
\yr 1967
\vol 6
\issue 2
\pages 35--47
\mathnet{http://mi.mathnet.ru/al1094}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=0218388}
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  • https://www.mathnet.ru/eng/al1094
  • https://www.mathnet.ru/eng/al/v6/i2/p35
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    Алгебра и логика Algebra and Logic
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