On the uniformity space in ZB-algebras


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Authors

  • Ahmed Talip Hussein Department of Mathematics, Faculty of Science, University of AL-Qadisiyah
  • Karrar Saad Hamzah Department of Mathematics, Faculty of Science, University of AL-Qadisiyah

Keywords:

b-algebra, sb-ideal, Uniform topology on B, zb-algebra, Topological zb-algebra.

Abstract

In this paper, we used sb-ideal of an zb-algebra B to make a uniform structure (B, ℜ) and then the part ℜ induce an uniform topology T in B. We demonstrated that the pair (B, ф) is a topological zb-algebra and discussed related properties. Finally, we presented the translation of space (B,TI) and studied some of its properties that we consider essential according to our knowledge

References

Neggers, J., Jun, Y. B., Hee, S. K., “On d-ideals in d-algebras”, Math. Slovaca, 49 (3), (1999), 243–251.

Young. B. J., Hee. S. K., “Uniform structures in positive implication algebras”, Int. Math. J., 2, (2002), 215–2.

Yoon, D. S., Kim, H. S., “Uniform structures in BCL – algebras”, Commun. Korean, Math.Soc., 17 (3), (2002), 403407,

https://doi.org/10.4134/CKMS.2002.17.3.403

Ahmed, T. H., Emad, A. S, “Some Properties of BP-Space”, Mathematics and Statistics, 10 (1), (2022), 195–200, https:// doi.org/10.13189/ms.2022.100118.

Habeeb, K., Haider, J., Ahmed, T., “Limit Sets and Cartan D – space”, Journal of AL-Qadisiyah for computer science and mathematics, 9 (2), (2017), 134–140, https://doi.org/10.29304 /jqcm.2017.9.2.305.

Ahmed, T. H., Habeeb, K. A., Haider, J., A, “Uniformity in d-algebras”, Earthline Journal of Mathematical Sciences, 2 (1), (2019), 207–221, https://doi.org/10.34198/ejms.2119.207221

Ahmed, T. H, “The orbits and minimal sets in d – algebra”, Journal of Physics: Conference Series, 1664, (2020), 1742– 6596, https://doi.org/10.1088/1742-6596/1664/1/012048

Sims B.T., “Fundamentals of Topology”, Macmillan Publishing Co., Inc., New York, (1976).

Yamini C., Kailasavalli S., “Fuzzy B – Ideals On B – algebra”, International, Journal of Mathematical Archive, 5 (2), (2014), 227–233, www.ijma.info

Neggers, J., Hee, S. K., “On B-algebras”, Mate. Vesnik, vol.54, pp.21-29, 2002.

Meng, J. Y. Jun, B., “BCK-algebras”, Kyung Moon Sa, Seoul, Korea, pp. 293–377, 1994. https://doi. org/10.1007/978-94-017-2422-7_6.

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Published

2023-10-19

How to Cite

Ahmed Talip Hussein, & Karrar Saad Hamzah. (2023). On the uniformity space in ZB-algebras. Results in Nonlinear Analysis, 6(3), 137–143. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/342