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Algebra Logika, 2013, Volume 52, Number 5, Pages 589–600 (Mi al605)  

Projections of monogenic algebras

S. S. Korobkov

Ural State Pedagogical University, ul. K. Libknekhta 9, Yekaterinburg, 620065, Russia

Abstract: Let $A$ and $B$ be associative algebras treated over a same field $F$. We say that the algebras $A$ and $B$ are lattice isomorphic if their subalgebra lattices $L(A)$ and $L(B)$ are isomorphic. An isomorphism of the lattice $L(A)$ onto the lattice $L(B)$ is called a projection of the algebra $A$ onto the algebra $B$. The algebra $B$ is called a projective image of the algebra $A$. We give a description of projective images of monogenic algebraic algebras. The description, in particular, implies that the monogeneity of algebraic algebras treated over a field of characteristic 0 is preserved under projections. Also we give an account of all monogenic algebraic algebras for which a projective image of the radical is not equal to the radical of a projective image.

Keywords: monogenic algebraic algebras, lattice isomorphisms of associative algebras.

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English version:
Algebra and Logic, 2013, 52:5, 392–399

Bibliographic databases:

UDC: 512.552
Received: 14.11.2012
Revised: 11.10.2013

Citation: S. S. Korobkov, “Projections of monogenic algebras”, Algebra Logika, 52:5 (2013), 589–600; Algebra and Logic, 52:5 (2013), 392–399

Citation in format AMSBIB
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\paper Projections of monogenic algebras
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\vol 52
\issue 5
\pages 589--600
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\jour Algebra and Logic
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\vol 52
\issue 5
\pages 392--399
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