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ArticleOriginal scientific text

Title

Frobenius n-group algebras

Authors 1

Affiliations

  1. Faculty of Science, University of Montenegro, P.O. Box 211, 8-1000 Podgorica, Serbia and Montenegro

Abstract

Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).

Keywords

ENG
n-ary group (n-group, polyadic group), (2,n)-ring, n-group-ring (algebra), (quasi-) Frobenius property, Artinianity property, regular bilinear from, descending chain condition for left (right) ideals, univeral enveloping (or covering) group, annhilator

Bibliography

  1. V.A. Artamonov, Free n-groups (Russian), Mat. Zametki 8 (1970), 499-507.
  2. L.A. Bokut, I.V. L'vov and V.K. Kharchenko, Nonkommutative Rings (Russian), vol. 18 of 'Itogi Nauki i Tekhniki', Izdat. VINITI, Moscov 1988.
  3. A.G. Kurosh, General Algebra. - Lectures of the 1969-1970 Academic Year (Russian), Izdat, 'Nauka', Moscov 1974.
  4. E.L. Post, Polyadic groups, Trans. Amer. Math. Soc. 48 (1940), 208-350.
  5. B. Zeković and V.A. Artamonov, n-Group rings and their radicals (Russian), Abelian Groups and Modules (Tomsk), 11 (1992), 3-7 (in Russian).
  6. B. Zeković and V.A. Artamonov, Connections betweem some properties of n-group rings and group rings (Russian), Math. Montisnigri 11 (1999), 151-158.
Discussiones Mathematicae - General Algebra and Applications
2002/22/2
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Pages:
153-159
Main language of publication
English
Received
2002-06-01
Published
2002

DOI: 10.7151/dmgaa.1054

Exact and natural sciences