On the properties of the Boolean algebras induced by a unital lattice ordered group

Document Type : Original Paper

Authors

1 ) Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

2 ) Faculty of Mathematics, Department of Science., University of Qom, Qom, Iran.

Abstract

In this paper we study the relations between unital lattice-ordered groups and Boolean algebras. At first we prove some main results about the properties of lattice-ordered groups. Then we see that every unital lattice-ordered group induces a Boolean algebra and we investigate some properties of the Boolean algebra. For instance, we prove that the Boolean algebra induced by the lattice-ordered group of all measurable real valued functions on a measure space, consists of all characteristic functions. We also see that in some cases, these Boolean algebras are trivial.

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References

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Journal of Advanced Mathematical Modeling
Volume 12, Issue 3
November 2022
Pages 372-382

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History

  • Receive Date: 08 May 2022
  • Revise Date: 27 August 2022
  • Accept Date: 03 September 2022

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