For citation:
Balaba I. N., Krasnova E. N. Полупростые градуированные кольца. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 23-28. DOI: 10.18500/1816-9791-2013-13-4-23-28
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
25.11.2013
Full text:
(downloads: 153)
Language:
Russian
Heading:
UDC:
512.522
Полупростые градуированные кольца
Autors:
Balaba Irina Nikolaevna, Tula State Pedagogical University,
Krasnova Ekaterina Nikolaevna, Tula State Pedagogical University,
Abstract:
The graded version ofWedderburn–Artin theorem is obtained. It gives description of semisimpleG-graded ring for arbitrary groupG. Homological classification of graded semisimple rings is given.
References:
- Nˇastˇasescu C., Oystaeyen F. van. Method of graded rings. Berlin, Springer, 2004, 295 p.
- Hwang Y.-S., Wadsworth A. R. Correspondences between valued division algebras and graded division algebras. J. Algebra, 1998, vol. 220, pp. 73–114.
- Bahturin Yu. A. Zaicev M. V., Sehgal S. K. Finite-dimensional simple graded algebras. Sbornik : Mathematics, 2008, vol. 199, no. 7, pp. 965–983. DOI:10.1070/SM2008v199n07ABEH003949
- Balaba I. N. Mikhalev A. V. Isomorphisms of graded endomorphism rings of graded modules close to free ones. J. Math. Sci., 2009, vol. 156, no. 2, pp. 209–218.
- Balaba I. N. Graduirovannye prostye artinovy kol’tsa [Graded simple artinian rings]. Algebra i matematicheskaia logika : materialy mezhdunar. konf., posviashch. 100-letiiu so dnia rozhdeniia prof. V. V. Morozova [Algebra and Mathematical Logika : Trans. Intern. Confer., dedicated to 100th anniversary of V. V. Morozov]. Kazan, 2011, pp. 43–44 (in Russian).
- Liu S.-X., Beattie M., Fang H. Graded division rings and the Jacobson density theorem. J. Beijing Normal University (Natural Science), 1991, vol. 27, no. 2, pp. 129–134.
- Balaba I. N. Izomorfizmy graduirovannykh kolets lineinykh preobrazovanii graduirovannykh vektornykh prostranstv [Isomorphisms of graded rings of linear transformations of graded vector spaces]. Chebyshevckiy sbornik, 2005, vol. 6. no. 4(16), pp. 6–23 (in Russian).
- Dˇascˇalescu S., Ion B., Nˇastˇasescu C., Rios Montes J. Group gradings on full matrix rings. J. Algebra, 1999, vol. 220, pp. 709–728.
- Bahturin Yu. A., Sehgal S.K., Zaicev M.V. Group graging on associative algebras. J. Algebra, 2001, vol. 241, pp. 677–698.
- Bahturin Ju. A., Zaicev M. V. Group gradings on matrix algebras. Canad. Math. Bulletin, 2002, vol. 45, pp. 499–508.
- Zalesskii A. E., Mikhalev A. V. Group rings. J. of Soviet Math., 1975, vol. 4, no. 1, pp. 1–78.
Short text (in English):
(downloads: 58)
- 902 reads