Structures of Pseudo - BG Algebra and Sime pseudo – BG - Algebra

Main Article Content

Shwan Adnan Bajalan
Rasti Raheem Mohammed Amin
Aram K. Bajalan

Abstract

In this paper, we introduced the notion new types of algebras pseudo BG- algebra, pseudo sub BG –algebra, Pseudo Ideal and pseudo strong Ideal of Pseudo-BG-Algebras. We state some Proposition and examples which determine the relationships between these notions and some types of ideal and we introduced the notion semi pseudo BG- algebra, pseudo sub BG –algebra, Pseudo Ideal and pseudo strong Ideal of semi   pseudo-BG-Algebras. We investigated a new notion, of algebra called semi pseudo BG- algebra. We state some Proposition and examples which determine the relationships between these notions and some types of ideals defined minimal and homomorphism and kernel.

Article Details

How to Cite
Shwan Adnan Bajalan, Rasti Raheem Mohammed Amin, & Aram K. Bajalan. (2022). Structures of Pseudo - BG Algebra and Sime pseudo – BG - Algebra. Tikrit Journal of Pure Science, 27(3), 73–77. https://doi.org/10.25130/tjps.v27i3.48
Section
Articles

References

[1] K. Iseki, On BCI-algebras, Math. Sem. Notes Kobe Univ.1 (1980), 125-130.

MR 81k:06018a. Zbl 0434.03049.

[2] K. Iseki, S. Tanaka, An introduction to the theory of BCK-algebras, Math.

Japon.1 (1978),1-26. MR 80a:03081. Zbl 385.03051.

[3] Q. L. Hu, X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ.2 (1983),part 2, 313-320. MR 86a:06016. Zbl 579.03047.

[4] Y. H. Kim, K. S. So, On minimality in pseudo-BCI-algebras, Commun. Korean Math. Soc.27 (2012), 7-13. doi:10.4134/CKMS.2012.27.1.007. [5] Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japon.4 (1985), 659-661. MR 87d:06042. Zbl 583.03050.

[6] 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.

[7] G. Georgescu, A. Iorgulescu, Pseudo-BCK algebras, an extension of BCK algebras, in: Proc. of DMTCS01: Combinatorics, Computability and Logic,Springer,London.(2001) 97-114.

[8] W. A. Dudek, Y. B. Jun, Pseudo-BCI-algebras, East Asian Math. J.24

(2008), 187-190.

[9] G. Georgescu, A. Iorgulescu, Pseudo-MV-algebras, a non-commutative extension of MV algebras, in: The Proc. of the Fourth International Symp. on Economic Informatics, Bucharest, Romania, May.1999 1999, 961-968.

[10] G. Georgescu, A. Iorgulescu, Pseudo-BL-algebras, a non-commutative extension of BL algebras, in: Abstracts of the Fifth International Conference FSTA; Slovakia, February. (2000), 90-92.

[11] G. Dymek, Atoms and ideals of pseudo-BCI-algebras, Comment. Math.52 (2012), 73-90.

[12] G. Dymek, p-semisimple pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput.19 (2012), 461-474.

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

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

[15] Y. B. Jun, H. S. Kim, J. Neggers, Pseudo-d-algebras, Information Sciences.179 (2009), 1751-1759. doi:10.1016/j.ins.2009.01.021.

[16] Sh. A. Bajalan, S. A. OZBAL, Some properties and homomorphisms of pseudo-Q algebras. J. Cont. Appl. Math. V. 6, p (3-17) (2017).

[17] J. Neggers, H.S. Kim, On B-algebras, in preparation.

[18] M. A. Chaudhry, On BCH-algebras, Math. Japonica.36 (1991), 665-676.

[19] S. S. Ahn, H. S. Kim On QS-algebras,J. Chungcheong Math. Soc.12. (1999), 33-41.

[20] C. B. Kim and H. S. Kim, ON BG-ALGEBRAS, Demonstratio Mathematica, Vo. XLI , no. 3, (2008)