On GE-algebras

Ravikumar Bandaru; Arsham Borumand Saeid; Young Bae Jun

doi:10.18778/0138-0680.2020.20

Authors

Ravikumar Bandaru GITAM (Deemed to be University), Department of Mathematics, Hyderabad Campus, Telangana-502329, India https://orcid.org/0000-0001-8661-7914
Arsham Borumand Saeid Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer, Kerman, Iran https://orcid.org/0000-0001-9495-6027
Young Bae Jun Gyeongsang National University, Department of Mathematics Educations, Jinju 52828, Korea http://orcid.org/0000-0002-0181-8969

DOI:

https://doi.org/10.18778/0138-0680.2020.20

Keywords:

(transitive) GE-algebra, filter, upper set, congruence kernel

Abstract

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

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