On GE-algebras

Ravikumar Bandaru; Arsham Borumand Saeid; Young Bae Jun

doi:10.18778/0138-0680.2020.20

On GE-algebras

Ravikumar Bandaru, Arsham Borumand Saeid, Young Bae Jun

Source

Bulletin of the Section of Logic > 2021 > 50 > 1 > 81-96

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.

Identifiers

journal ISSN :	2449-836X , 0138-0680
DOI	10.18778/0138-0680.2020.20

Authors

Ravikumar Bandaru

GITAM (Deemed to be University), Department of Mathematics, Hyderabad Campus, Telangana-502329, India

Arsham Borumand Saeid

Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer, Kerman, Iran

Young Bae Jun

Gyeongsang National University, Department of Mathematics Educations, Jinju 52828, Korea

Keywords

(transitive) GE-algebra filter upper set congruence kernel

Additional information

Publication languages: English

Data set: DML

Publisher

Wydawnictwo Uniwersytetu Łódzkiego

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Bibliography

[1] J. C. Abbott, Semi-boolean algebra, Matematički Vesnik, vol. 4(19) (1967), pp. 177–198.
[2] R. A. Borzooei, S. Khosravi Shoar, Implication algebras are equivalent to the dual implicative BCK-algebras, Scientiae Mathematicae Japonicae, vol. 63(3) (2006), pp. 429–431.
[3] R. A. Borzooei, J. Shohani, On generalized Hilbert algebras, Italian Journal of Pure and Applied Mathematics, vol. 29 (2012), pp. 71–86.

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Ravikumar Bandaru

Arsham Borumand Saeid

Young Bae Jun

Keywords

Additional information

Publisher

Fields of science

Fields of science

Bibliography

[1] J. C. Abbott, Semi-boolean algebra, Matematički Vesnik, vol. 4(19) (1967), pp. 177–198.

[2] R. A. Borzooei, S. Khosravi Shoar, Implication algebras are equivalent to the dual implicative BCK-algebras, Scientiae Mathematicae Japonicae, vol. 63(3) (2006), pp. 429–431.

[3] R. A. Borzooei, J. Shohani, On generalized Hilbert algebras, Italian Journal of Pure and Applied Mathematics, vol. 29 (2012), pp. 71–86.

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On GE-algebras