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On Boolean Subrings of Rings

  • Ivan Chajda
  • Günther Eigenthaler
Chapter

Abstract

We determine Boolean subrings of commutative unitary rings satisfying the identity \(x^{p+k} = x^{p}\) for some integer \(p \geq 1\) where k = 2 s or \(k = 2^{s} - 1\).

Keywords

Boolean ring Commutative unitary ring Characteristic 2 Subring 

MS Classification:

06E20 16R50 16B70 

Notes

Acknowledgements

This work is supported by ÖAD, Cooperation between Austria and Czech Republic in Science and Technology, Grant Number CZ 03/2013, and by the Project CZ1.07/2.3.00/20.0051 Algebraic Methods in Quantum Logics.

References

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    G. Birkhoff, Lattice Theory, 3rd edn. Colloquium Publications, vol. 25 (American Mathematical Society, Providence, 1967)Google Scholar
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    I. Chajda, F. Švrček, Lattice-like structures derived from rings. In Contributions to General Algebra, vol. 20 (Verlag Johannes Heyn, Klagenfurt, 2012), pp. 11–18Google Scholar
  3. 3.
    I. Chajda, F. Švrček, The rings which are Boolean. Discuss. Mathem. General Algebra Appl. 31, 175–184 (2011)CrossRefzbMATHGoogle Scholar
  4. 4.
    P. Jedlička, The rings which are Boolean II. Acta Univ. Carolinae (to appear)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Algebra and GeometryPalacký University OlomoucOlomoucCzech Republic
  2. 2.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienWienAustria

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