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Rings with polynomial identity and centrally essential rings

  • V. T. Markov
  • A. A. TuganbaevEmail author
Original Paper
  • 10 Downloads

Abstract

It is proved that for any prime integer p and each field F of characteristic p, there exists a centrally essential F-algebra which is not a PI-ring and is not algebraic over its center.

Keywords

Centrally essential ring PI ring Ring algebraic over its center Ring integral over its center 

Mathematics Subject Classification

16R99 16D10 

Notes

Acknowledgements

The authors are sincerely grateful to the reviewer for valuable comments and suggestions.

References

  1. Markov, V.T., Tuganbaev, A.A.: Centrally essential group algebras. J. Algebra. 518, 109–118 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Passman, D.S.: The Algebraic Structure of Group Rings. Wiley, New York (1977)zbMATHGoogle Scholar
  3. Rowen, L.H.: Polynomial Identities in Ring Theory. Academic Press, Inc., New York (1980)zbMATHGoogle Scholar
  4. Zhevlakov, K.A., Slin’ko, A.M., Shestakov, I.P., Shirshov, A.I.: Rings That are Nearly Associative, p. xi+371. Academic Press, New York (1982)zbMATHGoogle Scholar

Copyright information

© The Managing Editors 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.National Research University ”MPEI”Lomonosov Moscow State UniversityMoscowRussia

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