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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - S. S. Korobkov
TI  - Projections of monogenic algebras
JO  - Algebra i logika
PY  - 2013
SP  - 589
EP  - 600
VL  - 52
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2013_52_5_a4/
LA  - ru
ID  - AL_2013_52_5_a4
ER  - 
%0 Journal Article
%A S. S. Korobkov
%T Projections of monogenic algebras
%J Algebra i logika
%D 2013
%P 589-600
%V 52
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2013_52_5_a4/
%G ru
%F AL_2013_52_5_a4
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/

[1] D. W. Barnes, “Lattice isomorphisms of associative algebras”, J. Aust. Math. Soc., 6:1 (1966), 106–121 | DOI | MR | Zbl

[2] A. V. Yagzhev, “Reshëtochnaya opredelyaemost nekotorykh matrichnykh algebr”, Algebra i logika, 13:1 (1974), 104–116 | Zbl

[3] V. A. Lyatte, “O strukturno izomorfnykh nilpotentnykh algebrakh klassa tri”, Izv. AN BSSR. Ser. fiz.-matem., 1979, no. 5, 10–14 | MR | Zbl

[4] S. S. Korobkov, Reshëtochnye izomorfizmy assotsiativnykh nilalgebr, Dep. v VINITI, No 1519-80, Sverdl. gos. ped. in-t, Sverdlovsk, 1980, 44 pp.

[5] S. S. Korobkov, O proektirovaniyakh assotsiativnykh kommutativnykh nilpotentnykh algebr, Dep. v VINITI, No 1520-80, Sverdl. gos. ped. in-t, Sverdlovsk, 1980, 14 pp.

[6] S. S. Korobkov, “Reshëtochnye izomorfizmy algebraicheskikh algebr bez nilpotentnykh elementov”, Issledovaniya algebraicheskikh sistem po svoistvam ikh podsistem, Mezhvuz. sb., Ural. gos. un-t, Sverdlovsk, 1985, 75–84 | MR

[7] S. S. Korobkov, “O reshëtochnykh izomorfizmakh monogennykh kolets”, Problemy fiziko-matematicheskogo obrazovaniya v pedagogicheskikh vuzakh Rossii na sovremennom etape, Tez. dokl. nauch.-prakt. konf. vuzov Uralskoi zony (26–29 marta 2001 g., Chelyabinskii gos. ped. in-t), Chelyabinsk, 2001

[8] S. Leng, Algebra, Mir, M., 1968

[9] S. S. Korobkov, “Assotsiativnye koltsa s plotnoi reshëtkoi podkolets”, Issledovaniya algebraicheskikh sistem po svoistvam ikh podsistem, Mezhvuz. sb., Ural. gos. un-t, Sverdlovsk, 1987, 63–71 | MR

[10] N. Dzhekobson, Stroenie kolets, IL, M., 1961