Geodesic
Commutative products of linear $\Omega$-algebras
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 979-999.

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

In this paper we study $\mathbf P$-products of $\Omega$-algebras which are linear over some field. We characterize the subalgebras of the $\mathbf P$-products for the case when $\mathbf P$ consists of zero order commutative identities, and the subalgebra belongs to the manifold $\mathfrak M_{\mathbf P}$. We investigate the question of the structure of an arbitrary subalgebra of the $\mathbf P$-product, as well as some cases of $\mathbf P$-products for commutative identities of nonzero order. We look into the possibility of $\mathbf P$-decomposing a linear $\Omega$-algebra from an arbitrary manifold $\mathfrak M_{\mathbf S}$ and give necessary conditions for this. 
@article{IM2_1970_4_5_a1,
     author = {M. S. Burgin},
     title = {Commutative products of linear $\Omega$-algebras},
     journal = {Izvestiya. Mathematics },
     pages = {979--999},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a1/}
}
TY  - JOUR
AU  - M. S. Burgin
TI  - Commutative products of linear $\Omega$-algebras
JO  - Izvestiya. Mathematics 
PY  - 1970
SP  - 979
EP  - 999
VL  - 4
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a1/
LA  - en
ID  - IM2_1970_4_5_a1
ER  - 
%0 Journal Article
%A M. S. Burgin
%T Commutative products of linear $\Omega$-algebras
%J Izvestiya. Mathematics 
%D 1970
%P 979-999
%V 4
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a1/
%G en
%F IM2_1970_4_5_a1
M. S. Burgin. Commutative products of linear $\Omega$-algebras. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 979-999. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a1/

[1] Kurosh A. G., “Multioperatornye koltsa i algebry”, Uspekhi matem. nauk, 24:1 (1960), 3–15

[2] Kurosh A. G., “Svobodnye summy multioperatornykh algebr”, Sib. matem. zh., 1 (1960), 62–70 | MR | Zbl

[3] Gainov A. T., “Kommutativnye i antikommutativnye svobodnye proizvedeniya algebr”, Sib. matem. zh., 3 (1962), 805–833 | MR | Zbl

[4] Polin S. V., “Podalgebry svobodnykh algebr nekotorykh mnogoobrazii multioperatornykh algebr”, Uspekhi matem. nauk, 24:1 (1969), 17–26 | MR | Zbl

[5] Burgin M. S., “Teorema o svobode v nekotorykh mnogoobraziyakh lineinykh $\Omega$-algebr i $\Omega$-kolets”, Uspekhi matem. nauk, 24:1 (1964), 27–38 | MR

[6] Zhukov A. I., “Privedennye sistemy opredelyayuschikh sootnoshenii v algebrakh”, Matem. sb., 27 (1950), 267–280

[7] Shirshov A. I., “Podalgebry svobodnykh kommutativnykh i svobodnykh antikommutativnykh algebr”, Matem. sb., 34(76):1 (1954), 81–88 | MR | Zbl

[8] Kurosh A. G., “Neassotsiativnye svobodnye summy algebr”, Matem. sb., 37 (1955), 251–264 | Zbl

[9] Kon P., Universalnaya algebra, Mir, M., 1968 | MR

[10] Kizner F. I., “Dve teoremy o tozhdestvakh v multioperatornykh algebrakh”, Uspekhi matem. nauk, 24:1 (1969), 39–42 | MR | Zbl

[11] Baranovich T. M., “O politozhdestvakh v universalnykh algebrakh”, Sib. matem. zh., 5 (1964), 976–986 | Zbl