Quadratic BH-algebras and Quadratic TM-algebras

Article Sidebar

pdf
Published: Oct 25, 2023
DOI: https://doi.org/10.25130/tjps.v28i5.1585
Keywords:
BH-algebra, TM-algebra, algebra

Main Article Content

Shawn Adnan Bajalan
Department of Mathematics, College of Education, University of Garmian, Kurdistan Region -Iraq.
Mohammed Shahab Hassan
Department of Chemistry, College of Education, University of Garmian, Kurdistan Region -Iraq.
Aram K. Bajalan
Department of Mathematics, College of Education, University of Garmian, Kurdistan Region -Iraq.

Abstract

In this paper we present the notion of “quadratic” BH-algebra and TM-algebra, and show that every quadratic BH-algebra and TM-algebra  has a product of the form    , where ; if  is a field with  and  BCI-algebra. Moreover, we show some theorems and examples with relationships among B-algebra, BH –algebra, BG-algebra and TM-algebra.

Article Details

How to Cite
Bajalan, S. A., Hassan, M. S., & Bajalan, A. K. (2023). Quadratic BH-algebras and Quadratic TM-algebras. Tikrit Journal of Pure Science, 28(5), 176–181. https://doi.org/10.25130/tjps.v28i5.1585
Issue
Vol. 28 No. 5 (2023)
Section
Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.

References

[1] K. Iseki, an introduction to the theory of BCK-algebras, Math. Japan. (1978) - cir.nii.ac.jp

[2] K. Iseki, On BCI-algebras, Math. Sem. Notes Kobe Univ.1 (1980), 125-130. MR 81k:06018a.

[3] Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11 (1983), no. 2, part 2, 313–320. MR 86a:06016. Zbl 579.03047.

[4] Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japon. 30 (1985), no. 4, 659–661. MR 87d:06042. Zbl 583.03050.

[5] C. B. Kim and H. S. Kim, On BG-algebras, Mate. Vesnik 41 (2008), 497-505.

[6] Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math. 1(1998), 347–354.

[7] K. Megali and Dr.A. Tamilarasi, TM-algebra-Introduction,Casct(2010).

[8] J. Neggers and H. S. Kim, On B-algebras, Math. Vesnik 54 (2002), 21-29.

[9] N. Joseph, S. A. Sun, S.K. Hee, ON Q-ALGEBRAS, Hindawi Publishing Corp, IJMMS.27:12 (2001), 749-757 PII.S0161171201006627. http://ijmms.hindawi.com.

[10] H. K. Park and H. S. Kim, On quadratic B-algebras, Quasigroups and Related Sys., 7(2001), 67-72.

[11] H. S. Kim and H. D. Lee, A quadratic BG-algebras, Int. Math. J. 5 (2004), 529-535.

[12] H. S. Kim and Na Ri KYE, On Quadratic BF-algebras, Sci. Math. Japon., (2006), 1171-1174.

[13] Sun Shin Ahn and Jeong Soon Han , On BP-algebras , journal mathematics and statistcs,5(2013),551-557.

[14] K. J. Lee, Ch. H. Park, Some ideals of pseudo-BCI-algebras, J.Appl.Informatics.27 (2009), 217-231.