Geodesic
Projections of monogenic algebras
Algebra i logika, Tome 52 (2013) no. 5, pp. 589-600

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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. 
@article{AL_2013_52_5_a4,
     author = {S. S. Korobkov},
     title = {Projections of monogenic algebras},
     journal = {Algebra i logika},
     pages = {589--600},
     publisher = {mathdoc},
     volume = {52},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_5_a4/}
}
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S. S. Korobkov. Projections of monogenic algebras. Algebra i logika, Tome 52 (2013) no. 5, pp. 589-600. http://geodesic.mathdoc.fr/item/AL_2013_52_5_a4/