Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FPM_2012_17_2_a0, author = {I. N. Balaba and A. L. Kanunnikov and A. V. Mikhalev}, title = {Quotient rings of graded associative {rings.~I}}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {3--74}, publisher = {mathdoc}, volume = {17}, number = {2}, year = {2012}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a0/} }
TY - JOUR AU - I. N. Balaba AU - A. L. Kanunnikov AU - A. V. Mikhalev TI - Quotient rings of graded associative rings.~I JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2012 SP - 3 EP - 74 VL - 17 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a0/ LA - ru ID - FPM_2012_17_2_a0 ER -
I. N. Balaba; A. L. Kanunnikov; A. V. Mikhalev. Quotient rings of graded associative rings.~I. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 3-74. http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a0/
[1] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Faktorial, M., 2003
[2] Balaba I. N., “Koltsa chastnykh polupervichnykh graduirovannykh kolets”, Tr. mezhdunar. seminara “Universalnaya algebra i eë prilozheniya”, Volgograd, 2000, 21–28
[3] Balaba I. N., “Izomorfizmy graduirovannykh kolets lineinykh preobrazovanii graduirovannykh vektornykh prostranstv”, Chebyshëvskii sb., 6:4(16) (2005), 6–23 | MR
[4] Balaba I. N., “Graduirovannye regulyarnye koltsa i moduli”, Chebyshëvskii sb., 11:3(35) (2010), 22–31 | MR | Zbl
[5] Balaba I. N., Efremov V. A., “Graduirovannye koltsa chastnykh polupervichnykh graduirovannykh kolets”, Chebyshëvskii sb., 11:1(33) (2010), 20–30 | MR | Zbl
[6] Balaba I. N., Zelenov S. V., Limarenko S. V., Mikhalëv A. V., “Teoremy plotnosti dlya graduirovannykh kolets”, Fundament. i prikl. mat., 9:1 (2003), 27–49 | MR | Zbl
[7] Balaba I. N., Mikhalëv A. V., “Izomorfizmy i antiizomorfizmy kolets endomorfizmov graduirovannykh modulei, blizkikh k svobodnym”, Dokl. RAN, 425:5 (2009), 583–586 | MR | Zbl
[8] Bakhturin Yu. A., Zaitsev M. V., Segal S. K., “Konechnomernye prostye graduirovannye algebry”, Mat. sb., 199:7 (2008), 21–40 | DOI | MR
[9] Beidar K. I., “Koltsa s obobschënnymi tozhdestvami. I”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1977, no. 2, 19–26 | MR | Zbl
[10] Bovdi A. A., Gruppovye koltsa, Izd-vo Uzhgorod. un-ta, Uzhgorod, 1974 | MR
[11] Dzhekobson N., Stroenie kolets, Izd. inostr. lit., M., 1961 | MR
[12] Zaitsev M. V., Segal S. K., “Konechnye graduirovki prostykh artinovykh kolets”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2001, no. 3, 21–24 | MR | Zbl
[13] Zalesskii A. E., Mikhalëv A. V., “Gruppovye koltsa”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 2, 1973, 5–118 | MR | Zbl
[14] Zelmanov E. I., “Teoremy Goldi dlya iordanovykh algebr”, Sib. mat. zhurn., 28:6 (1987), 44–52 | MR
[15] Zelmanov E. I., “Teoremy Goldi dlya iordanovykh algebr. II”, Sib. mat. zhurn., 29:4 (1988), 68–74 | MR
[16] Kanunnikov A. L., “Graduirovannye varianty teoremy Goldi”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2011, no. 3, 46–50 | MR
[17] Lambek I., Koltsa i moduli, Mir, M., 1971 | MR | Zbl
[18] Limarenko S. V., “Slabo primitivnye superkoltsa”, Fundament. i prikl. mat., 10:3 (2004), 97–142 | MR | Zbl
[19] Rakhman M. T., In'ektivnye moduli, koltsa endomorfizmov i lokalizatsii v sluchae graduirovannykh kolets, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1982
[20] Tuganbaev A. A., Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009
[21] Feis K., Algebra: koltsa, moduli i kategorii, v. 1, Mir, M., 1977
[22] Kherstein I., Nekommutativnye koltsa, Mir, M., 1972 | MR
[23] Elmakhdi S. S., Graduirovannye regulyarnye koltsa i graduirovannye $V$-moduli, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1985
[24] Amitsur S. A., “On rings of quotients”, Symp. Math., 8 (1972), 149–164 | MR | Zbl
[25] Anquela J. A., García E., Gómez-Lozano M., “Maximal algebras of Martindale-like quotients of strongly prime linear Jordan algebras”, J. Algebra, 280 (2004), 367–383 | DOI | MR | Zbl
[26] Aranda Pino G., Siles Molina M., “The maximal graded left quotient algebra of a graded algebra”, Acta Math. Sinica. Eng. Ser., 22:21 (2006), 261–275 | DOI | MR
[27] Asano K., “Arithmetische Idealtheorie in nichtkommutativen Ringen”, Japan J. Math., 15 (1939), 1–36 | MR
[28] Bahturin Yu. A., Sehgal S. K., Zaicev M. V., “Group graging on associative algebras”, J. Algebra, 241 (2001), 677–698 | DOI | MR | Zbl
[29] Beidar K. I., Martindale W. S., Mikhalev A. V., Rings with Generalized Identities, Marcel Dekker, New York, 1996 | MR | Zbl
[30] Bell A. D., “Localization and ideal theory in Noetherian strongly group-graded rings”, J. Algebra, 105 (1987), 76–115 | DOI | MR | Zbl
[31] Burgess W. D., “Rings of quotients of group rings”, Can. J. Math., 21 (1969), 865–875 | DOI | MR | Zbl
[32] Cohen M., Rowen L. H., “Group-graded rings”, Commun. Algebra, 11:1 (1983), 1253–1270 | DOI | MR | Zbl
[33] Cohn P., “Simple rings without zero-divisors and Lie division rings”, Matematika, 6 (1959), 14–18 | DOI | MR | Zbl
[34] Dǎscǎlescu S., Ion B., Nǎstǎsescu C., Rios Montes J., “Group gradings on full matrix rings”, J. Algebra, 220 (1999), 709–728 | DOI | MR
[35] Ferrero M., Jespers E., Puezylowski E. R., “Prime ideals of graded rings and related matter”, Commun. Algebra, 18:11 (1990), 3819–3834 | DOI | MR | Zbl
[36] Fošner M., “On the extended centroid of prime associative superalgebras with applications to superderivations”, Commun. Algebra, 32:2 (2004), 689–705 | DOI | MR
[37] Gabriel P., “La localisation dans les anneaux non commutatifs”, Séminaire Dubreil. Algèbre et théorie des nombres, 13:1, exp. 2 (1959–1960), 1–35 | MR
[38] Gabriel P., “Des categories abeliennes”, Bull. Soc. Math. Fr., 90 (1962), 323–448 | MR | Zbl
[39] Goldie A. W., “The structure of prime rings under ascending chain conditions”, Proc. London Math. Soc., 8 (1958), 589–608 | DOI | MR | Zbl
[40] Goldie A. W., “Semi-prime rings with maximal conditions”, Proc. London Math. Soc., 10 (1960), 201–220 | DOI | MR | Zbl
[41] Goldie A. W., “Non-commutative principal ideal rings”, Arch. Math., 13 (1962), 213–221 | DOI | MR | Zbl
[42] Goodearl K., Stafford T., “The graded version of Goldie's theorem”, Contemp. Math., 259 (2000), 237–240 | DOI | MR | Zbl
[43] Jategaonkar A. V., Left Principal Ideal Rings, Lect. Notes Math., 123, Springer, Berlin, 1970 | MR | Zbl
[44] Jensen A., Jondrup S., “Classical quotient rings of group graded rings”, Commun. Algebra, 20 (1992), 2923–2936 | DOI | MR | Zbl
[45] Jespers E., “Jacobson rings and rings strongly graded by an Abelian group”, Israel J. Math., 63 (1988), 67–78 | DOI | MR | Zbl
[46] Jespers E., “Computing the extended centroid of Abelian-group graded-rings”, Commun. Algebra, 20:12 (1992), 3603–3608 | DOI | MR | Zbl
[47] Jespers E., Wauters P., “A general notion of noncommutative Krull rings”, J. Algebra, 112 (1988), 388–415 | DOI | MR | Zbl
[48] Johnson R. E., “The extended centralizer of a ring over a module”, Proc. Amer. Math. Soc., 2 (1951), 891–895 | DOI | MR | Zbl
[49] Lambek J., “On structure of semi-prime rings and their rings of quotients”, Can. J. Math., 13 (1961), 392–417 | DOI | MR | Zbl
[50] Lambek J., “On Utumi's rings of quotients”, Can. J. Math., 15 (1963), 363–370 | DOI | MR | Zbl
[51] Liu S., Beattie M., Fang H., “Graded division rings and the Jacobson density theorem”, J. Beijing Normal Univ. (Natur. Sci.), 27:2 (1991), 129–134 | MR | Zbl
[52] Martindale W. S., “Prime rings satisfying a generalized polynomial identity”, J. Algebra, 12 (1969), 576–584 | DOI | MR | Zbl
[53] Nǎstǎsescu C., “Some constructions over graded rings. Application”, J. Algebra, 120 (1989), 119–138 | DOI | MR
[54] Nǎstǎsescu C., Nauwelaerts E., van Oystaeyen F., “Arithmetically graded rings revisited”, Commun. Algebra, 14:10 (1986), 1191–2017 | MR
[55] Nǎstǎsescu C., van Oystaeyen F., Graded and Filtered Rings and Modules, Lect. Notes Math., 758, Springer, Berlin, 1979 | MR
[56] Nǎstǎsescu C., van Oystaeyen F., Graded Ring Theory, North-Holland, Amsterdam, 1982 | MR
[57] Nǎstǎsescu C., van Oystayen F., Graded Ring Theory, North-Holland, Amsterdam, 2004
[58] Ore O., “Linear equations in non-commutative fields”, Ann. Math., 32 (1931), 463–477 | DOI | MR | Zbl
[59] Van Oystaeyen F., “Note on graded von Neumann regular rings”, Rev. Roumaine Math. Pures Appl., 29:3 (1984), 263–271 | MR | Zbl
[60] Passman D. S., “Computing the symmetric rings of quotients”, J. Algebra, 105 (1987), 207–235 | DOI | MR | Zbl
[61] Siles Molina M., “Algebras of quotients of Lie algebras”, J. Pure Appl. Algebra, 188 (2004), 175–188 | DOI | MR | Zbl
[62] Stenström B., Rings of Quotients. An Introduction to Methods of Ring Theory, Springer, Berlin, 1975 | MR | Zbl
[63] Utumi Y., “On quotient rings”, Osaka J. Math., 8 (1956), 1–18 | MR | Zbl
[64] Yahya H., “A note on graded regular rings”, Commun. Algebra, 25:1 (1997), 223–228 | DOI | MR | Zbl