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 provide a characterization of all monogenic algebraic algebras for which a projective image of the radical is not equal to the radical of a projective image.
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Translated from Algebra i Logika, Vol. 52, No. 5, pp. 589-600, September-October, 2013.
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Korobkov, S.S. Projections of Monogenic Algebras. Algebra Logic 52, 392–399 (2013). https://doi.org/10.1007/s10469-013-9251-8
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DOI: https://doi.org/10.1007/s10469-013-9251-8