Geodesic
A general version of standard bases in associative algebras and their universal constructions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 183-203 
V. N. Latyshev. A general version of standard bases in associative algebras and their universal constructions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 183-203. http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This work is devoted, in some sense, to “methodical” questions. A general version of standard basis in ideal of algebra is presented which uses a notion of so called algebra with a strong filtration introduced recently by the author. Moreover, universal constructions related this class of algebras such as direct sums, tensor products, and free modules are considered.

[1] Latyshev V. N., “Algebry so strogoi filtratsiei i standartnye bazisy”, Tr. Mat. tsentra im. N. I. Lobachevskogo, 12, Kazan, 2001, 3–18 | MR

[2] Latyshev V. N., “Proizvodnye struktury algebr so strogoi filtratsiei”, Mat. metody i prilozheniya, Tr. 9-kh mat. chtenii MGSU, M., 2001, 124–127

[3] Shirshov A. I., “Nekotorye algoritmicheskie problemy v algebrakh Li”, Sib. mat. zhurn., 1:3 (1962), 292–296

[4] Shirshov A. I., “O bazakh svobodnoi algebry Li”, Algebra i logika, 1:1 (1962), 14–19 | MR | Zbl

[5] Bergman G., “The diamond lemma for ring theory”, Adv. Math., 29:2 (1978), 178–218 | DOI | MR

[6] Bergman G., “Ordering coproducts of groups and semigroups”, J. Algebra, 133:2 (1990), 313–339 | DOI | MR | Zbl

[7] Buchberger B., “Gröbner bases: An algorithmic method in polynomial ideal theory”, Multidimensional Systems Theory – Progress, Directions and Open Problems, ed. N. K. Bose, Reidel, Dordrecht, 1985, 184–232 | DOI | Zbl

[8] Gerdt V. P., Blinkov Yu. A., “Involutive bases of polynomial ideals”, Math. Comput. Simulation, 45 (1998), 519–542 | DOI | MR

[9] Golod E. S., “Standard bases and homology”, Algebra: Some Current Trends, Proc. 5th Natl. Sch. Algebra (Varna/Bulg., 1986), Lect. Notes Math., 1352, Springer, Berlin, 1988, 88–95 | DOI | MR

[10] Latyshev V. N., “Canonization and standard bases of filtered structures”, Lie Algebras, Rings and Related Topics, Papers of the 2nd Tainan–Moscow Int. Algebra Workshop' 97 (Tainan, Taiwan, January 11–17, 1997), ed. Y. Fong, Springer, Hong Kong, 2000, 61–79 | MR | Zbl

[11] Latyshev V. N., “An improved version of standard bases”, Formal Power Series and Algebraic Combinatorics, Proc. of the 12th Int. Conf., FPSAC' 00 (Moscow, Russia, June 26–30, 2000), ed. D. Krob, Springer, Berlin, 2000, 496–506 | DOI | MR

[12] Mikhalev A. A., “The composition lemma for color Lie superalgebras and for Lie $p$-algebras”, Algebra, Proc. Int. Conf. Memory A. I. Mal'cev, Pt. 2 (Novosibirsk/USSR, 1989), Contemp. Math., 131, Amer. Math. Soc., 1992, 91–104 | DOI | MR