Extension of stabilizers on subtraction algebras

Document Type : Special Issue Dedicated to Prof. Esfandiar Eslami

Authors

1 Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, Iran

2 ASU School of Computing and Augmented Intelligence, Tempe, AZ, USA

Abstract

This paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The study reveals that both the stabilizer of a subset and the stabilizer of an ideal with respect to another ideal are, in fact, ideals themselves. Investigating the impact of stabilizers on product and quotient subtraction algebras is a focal point. Additionally, a novel concept termed the ”stabilizer operation” is defined, and it is proven that the collection of ideals endowed with a binary stabilizer operator forms a bounded Hilbert algebra.

Keywords

Main Subjects

References

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Journal of Mahani Mathematical Research
Volume 13, Issue 4 - Serial Number 29
Special issue dedicated to Professor Esfandiar Eslami
December 2024
Pages 165-179

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History

  • Receive Date: 29 March 2024
  • Revise Date: 22 June 2024
  • Accept Date: 18 August 2024

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