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 = 2s or \(k = 2^{s} - 1\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G. Birkhoff, Lattice Theory, 3rd edn. Colloquium Publications, vol. 25 (American Mathematical Society, Providence, 1967)
I. Chajda, F. Švrček, Lattice-like structures derived from rings. In Contributions to General Algebra, vol. 20 (Verlag Johannes Heyn, Klagenfurt, 2012), pp. 11–18
I. Chajda, F. Švrček, The rings which are Boolean. Discuss. Mathem. General Algebra Appl. 31, 175–184 (2011)
P. Jedlička, The rings which are Boolean II. Acta Univ. Carolinae (to appear)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Chajda, I., Eigenthaler, G. (2014). On Boolean Subrings of Rings. In: Fontana, M., Frisch, S., Glaz, S. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0925-4_6
Download citation
DOI: https://doi.org/10.1007/978-1-4939-0925-4_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0924-7
Online ISBN: 978-1-4939-0925-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)