Geodesic
Some properties of subalgebras in varieties of linear $\Omega$-albebras
Sbornik. Mathematics, Tome 16 (1972) no. 1, pp. 69-85 
M. S. Burgin; V. A. Artamonov. Some properties of subalgebras in varieties of linear $\Omega$-albebras. Sbornik. Mathematics, Tome 16 (1972) no. 1, pp. 69-85. http://geodesic.mathdoc.fr/item/SM_1972_16_1_a5/
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     title = {Some properties of subalgebras in varieties of linear $\Omega$-albebras},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper studies connections between the Nielsen and Schreier properties in varieties of linear $\Omega$-algebras, and also between systems $S$ of identical relations such that the theorem about subalgebras lying in the variety $\mathfrak M_S$ is valid, or such that the theorem about finitely generated subalgebras analogous to that of Zhukov is valid. Bibliography: 17 titles.

[1] A. G. Kurosh, “Multioperatornye koltsa i algebry”, Uspekhi matem. nauk, XXIV:1(145) (1969), 3–15

[2] J. Lewin, “On Scheier varieties of lineare algebras”, Trans. Amer. Math. Soc., 132:2 (1968), 553–562 | DOI | MR | Zbl

[3] M. S. Burgin, “Teorema o svobode v nekotorykh mnogoobraziyakh lineinykh $\Omega$-algebr i $\Omega$-kolets”, Uspekhi matem. nauk, XXIV:1(145) (1969), 27–38 | MR

[4] A. G. Kurosh, Teoriya grupp, Nauka, Moskva, 1967 | MR | Zbl

[5] P. Kon, Universalnaya algebra, Mir, Moskva, 1968 | MR

[6] F. I. Kizner, “Dve teoremy o tozhdestvakh v multioperatornykh algebrakh”, Uspekhi matem. nauk, XXIV:1(45) (1969), 39–42 | MR

[7] A. G. Kurosh, Lektsii po obschei algebre, Fizmatgiz, Moskva, 1962 | MR

[8] A. Karras, D. Solitar, W. Magnus, Combinatorial group theory, John Wiley and Sons, New York, 1966 | Zbl

[9] M. S. Burgin, “Svobodnye epimorfnye obrazy svobodnykh lineinykh $\Omega$-algebr”, Tezisy dokladov po algebre, matem. logike i vychislitelnoi matematike konferentsii pedagogicheskikh vuzov tsentralnoi zony RSFSR, Ivanovo, 1970, 105–106

[10] M. S. Burgin, “Perestanovochnye proizvedeniya lineinykh $\Omega$-algebr”, Izv. AN SSSR. Ceriya matem., 34 (1970), 977–999 | MR | Zbl

[11] A. T. Gainov, “Kommutativnye svobodnye i antikommutativnye svobodnye proizvedeniya algebr”, Sib. matem. zh., 3:6 (1962), 805–833 | MR | Zbl

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

[13] A. I. Zhukov, “Neassotsiativnye svobodnye razlozheniya algebr s konechnym chislom obrazuyuschikh”, Matem. sb., 26(68) (1950), 471–478

[14] A. G. Kurosh, “Neassotsiativnye svobodnye summy algebr”, Matem. sb., 37(79) (1955), 251–264 | Zbl

[15] P. M. Cohn, “Subalgebras of free associative algebras”, Proc. London Math. Soc., 14 (1964), 618–632 | DOI | MR | Zbl

[16] A. G. Kurosh, “Neassotsiativnye svobodnye algebry i svobodnye proizvedeniya algebr”, Matem. sb., 20(62) (1947), 239–262 | MR | Zbl

[17] A. I. Shirshov, “Podalgebry svobodnykh lievykh algebr”, Matem. sb., 33(75) (1953), 441–452 | Zbl