Geodesic
Malcev rings
Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 63-81
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In the paper, Malcev rings are defined. The class of Malcev rings strictly contains rings of Malcev–Neumann series, formal skew Laurent series rings, and formal pseudo-differential operator rings. In the paper, ring-theoretic properties of Malcev rings are studied. It turns out that rings of Malcev–Neumann series, formal skew Laurent series rings, and formal pseudo-differential operator rings have similar ring-theoretic properties related to the existence of the filtration with respect to the lowest degree of the series. 
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D. A. Tuganbaev. Malcev rings. Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 63-81. http://geodesic.mathdoc.fr/item/DM_2008_20_2_a5/

[1] Benhissi A., Les anneaux de séries formelles, Queen's Papers in Pure and Applied Mathematics, 124, Queen's Univ., Kingston, 2003 | MR | Zbl

[2] Bergman G. M., “Conjugates and $n$th roots in Hahn–Laurents group rings”, Bull. Malaysian Math. Soc., 1:2 (1978), 29–41 | MR | Zbl

[3] Brookfield G., “Noetherian generalized power series rings”, Commun. Algebra, 32:3 (2004), 919–926 | DOI | MR | Zbl

[4] Faith C., Algebra: rings, modules, and categories, Vol. I, Springer, Berlin, 1973 | MR | Zbl

[5] Goodearl K. R., “Centralizers in differential, pseudo-differential, and fractional differential operator rings”, Rocky Mountain J. Math., 13:4 (1983), 573–618 | MR | Zbl

[6] Goodearl K. R., Small L. W., “Krull versus global dimension in Noetherian PI-rings”, Proc. Amer. Math. Soc., 92:2 (1984), 175–178 | DOI | MR | Zbl

[7] Goodearl K. R., Warfield R. B., An introduction to noncommutative Noetherian rings, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[8] Liu Z., “The ascending chain condition for principal ideals of rings of generalized power series”, Commun. Algebra, 32:9 (2004), 3305–3314 | DOI | MR | Zbl

[9] Liu Z., Ahsan J., “The Tor-groups of modules of generalized power series”, Algebra Colloq., 12:3 (2005), 477–484 | MR | Zbl

[10] Lorenz M., “Division algebras generated by finitely generated nilpotent groups”, J. Algebra, 85 (1983), 368–381 | DOI | MR | Zbl

[11] Makar-Limanov L., “The skew field of fractions of the first Weyl algebra contains a free noncommutative subalgebra”, Commun. Algebra, 11:17 (1983), 2003–2006 | DOI | MR | Zbl

[12] Maltsev A. I., “O vlozhenii gruppovykh algebr v tela”, Dokl. AH SSSR, 60 (1948), 1499–1501

[13] Musson I., Stafford K., “Malcev–Neumann group rings”, Commun. Algebra, 21:6 (1993), 2065–2075 | DOI | MR | Zbl

[14] Neumann B. H., “On ordered division rings”, Trans. Amer. Math. Soc., 66 (1949), 202–252 | DOI | MR | Zbl

[15] Parshin A. N., “O koltse formalnykh psevdodifferentsialnykh operatorov”, Trudy Matem. in-ta im. V. A. Steklova, 224, Nauka, M., 1999, 291–305 | MR

[16] Pommersheim J., Shahriari Sh., “Unique factorization in generalized power series rings”, Proc. Amer. Math. Soc., 134:5 (2006), 1277–1287 | DOI | MR | Zbl

[17] Ribenboim P., “Semisimple rings and von Neumann regular rings of generalized power series”, J. Algebra, 198:2 (1997), 327–338 | DOI | MR | Zbl

[18] Risman L., “Twisted rational functions and series”, J. Pure Appl. Algebra, 12 (1978), 181–199 | DOI | MR | Zbl

[19] Schur I., “Über vertauschbare lineare Differentialausdrücke”, Sitzungsber. Berliner Math. Ges., 4 (1905), 2–8 | Zbl

[20] Smits T. H., “Skew-Laurent series over semisimple rings”, Delft. Progr. Rep., 2 (1977), 131–136 | MR | Zbl

[21] Sonin K. I., “Regulyarnye koltsa ryadov Lorana”, Fundamentalnaya i prikladnaya matematika, 1:1 (1995), 315–317 | MR | Zbl

[22] Sonin K. I., “Regulyarnye koltsa kosykh ryadov Lorana”, Fundamentalnaya i prikladnaya matematika, 1:2 (1995), 565–568 | MR | Zbl

[23] Sonin K. I., “Biregulyarnye koltsa ryadov Lorana”, Vestnik Moskovskogo Universiteta, ser. matem. mekh., 1997, no. 4, 22–24 | MR

[24] Sonin C., “Krull dimension of Malcev–Neumann rings”, Commun. Algebra, 26:9 (1998), 2915–2931 | DOI | MR | Zbl

[25] Tuganbaev A. A., “Radikal Dzhekobsona koltsa ryadov Lorana”, Fundamentalnaya i prikladnaya matematika, 12:2 (2006), 209–216

[26] Tuganbaev D. A., “Tsepnye koltsa ryadov Lorana”, Fundamentalnaya i prikladnaya matematika, 3:3 (1997), 947–951 | MR | Zbl

[27] Tuganbaev D. A., “Tsepnye koltsa kosykh ryadov Lorana”, Vestnik Moskovskogo Universiteta, ser. matem. mekh., 2000, no. 1, 52–55 | MR | Zbl

[28] Tuganbaev D. A., “Koltsa kosykh ryadov Lorana i koltsa glavnykh idealov”, Vestnik Moskovskogo Universiteta, ser. matem. mekh., 2000, no. 5, 55–57 | MR | Zbl

[29] Tuganbaev D. A., “Some ring and module properties of skew power series”, Formal Power Series and Algebraic Combinatorics, Springer, Berlin, 2000, 613–622 | MR | Zbl

[30] Tuganbaev D. A., “Polulokalnye distributivnye koltsa kosykh ryadov Lorana”, Fundamentalnaya i prikladnaya matematika, 6:3 (2000), 913–921 | MR | Zbl

[31] Tuganbaev D. A., “Koltsa psevdodifferentsialnykh operatorov i usloviya na tsepi”, Vestnik Moskovskogo Universiteta, ser. matem. mekh., 2002, no. 4, 26–32 | MR | Zbl

[32] Tuganbaev D. A., “Laurent series rings and pseudo-differential operator rings”, J. Math. Sci., 128:3 (2005), 2843–2893 | DOI | MR | Zbl

[33] Tuganbaev D. A., “Loranovskie koltsa”, Fundamentalnaya i prikladnaya matematika, 12:3 (2006), 151–224 | MR