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|Title:||Projections of Monogenic Algebras|
|Authors:||Korobkov, S. S.|
|Citation:||Korobkov S. S. Projections of Monogenic Algebras / S. S. Korobkov // Algebra and logic. — 2013. — Vol. 52, iss. 5. — P. 392-399.|
|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 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.|
|Keywords:||MONOGENIC ALGEBRAIC ALGEBRAS|
LATTICE ISOMORPHISMS OF ASSOCIATIVE ALGEBRAS
|Appears in Collections:||Научные публикации, проиндексированные в Scopus и Web of Science|
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