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Mathematics. Mechanics. Informatics

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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

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Полупростые градуированные кольца

Balaba Irina Nikolaevna, Tula State Pedagogical University,
Krasnova Ekaterina Nikolaevna, Tula State Pedagogical University,

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.

  1. Nˇastˇasescu C., Oystaeyen F. van. Method of graded rings. Berlin, Springer, 2004, 295 p.
  2. Hwang Y.-S., Wadsworth A. R. Correspondences between valued division algebras and graded division algebras. J. Algebra, 1998, vol. 220, pp. 73–114.
  3. 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
  4. 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.
  5. 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).
  6. 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.
  7. 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).
  8. Dˇascˇalescu S., Ion B., Nˇastˇasescu C., Rios Montes J. Group gradings on full matrix rings. J. Algebra, 1999, vol. 220, pp. 709–728.
  9. Bahturin Yu. A., Sehgal S.K., Zaicev M.V. Group graging on associative algebras. J. Algebra, 2001, vol. 241, pp. 677–698.
  10. Bahturin Ju. A., Zaicev M. V. Group gradings on matrix algebras. Canad. Math. Bulletin, 2002, vol. 45, pp. 499–508.
  11. Zalesskii A. E., Mikhalev A. V. Group rings. J. of Soviet Math., 1975, vol. 4, no. 1, pp. 1–78.
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