On BDM-Algebras
DOI:
https://doi.org/10.31185/wjcm.101Keywords:
B-algebras, BD-algebras, BM-algebras, BF-algebras, BG-algebrasAbstract
Abstract algebra is one of the influential branches in the field of pure Mathematics. This field concentrate on the study of the algebraic structures and discussed the relationships among them. Many studies have been presented various types of algebraic structures some of which independently and some others have been constructed via extending form other algebraic structure in order to investigate some of their properties. In this paper, we established an algebraic structure namely BDM-Algebras and studied some of its properties. Furthermore, we presented the 0-commtativity, sub-algebra and normal sub-algebra of a BDM-Algebras. In addition, we provided BDM-homomorphism and the kernel of BDM-homomorphism with some properties of them. Moreover, we introduced the quotient BDM-Algebras by using the notation of normal ideal of BDM-Algebras. Finally, we introduced the concept of the direct product of BDM-Algebras and some of its properties have been discussed. Some examples are given to illustrated the results.
References
J. Neggers and H. S. Kim, “On B-algebras,” Mat. Vesnik, vol. 54, pp. 21–29, 2002.
C. B. Kim and H. S. Kim, “On BM-Algebras,” Scientiae Mathematicae Japonicae, pp. 215–221, 2006.
H. S. Kim and Y. H. Kim, “On BE-Algebras,” Scientiae Mathematicae Japonicae, pp. 1299–1302, 2006.
A. Walendziak, “On BF-Algebras,” Mathematica Slovaca, vol. 57, no. 2, pp. 119–128, 2007.
C. B. Kim and H. S. Kim, “On BG-Algebras,” Demonstration Mathematica, vol. 41, no. 3, pp. 497–505, 2008.
L. S. Mahdi and A. H. Nouri, “On BD-Algebra,” 1st International Virtual Conference on Pure Science. Journal of Physics: Conference series, pp. 1–13, 2020.
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Copyright (c) 2023 Mohammed Khalid Shahoodh
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