Pseudo-UP Ideals and Pseudo-UP Filters in Pseudo-UP Algebras

Year 2020, Volume: 8 Issue: 1, 155 - 158, 20.03.2020

Daniel A. Romano

https://doi.org/10.36753/mathenot.630110

Cited By: 4

Abstract

The notion of pseudo-UP algebras is introduced and analyzed in our forthcoming article as a generalization of UP-algebras.
In this article, as a continuation of the foregoing, we introduce and analyze concepts of pseudo-UP ideals and pseudo-UP filters in pseudo-UP algebras.

Keywords

UP-algebra, Pseudo-UP algebra, Pseudo-UP filter, Pseudo-UP ideal

References

• W. A. Dudek and Y. B. Jun. Pseudo-BCI algebras. East Asian Math. J., 24(2)(2008), 187-–190.
• G. Dymek. Atoms and ideals of pseudo-BCI-algebras. Comment. Math., 52(1)(2012), 73-–90.
• G. Georgescu and A. Iorgulescu. Pseudo-BCK algebras: An extension of BCK-algebras. Combinatorics, computability and logic (Constanta, 2001)}, (pp. 97-–114), Springer Ser. Discrete Math. Theor. Comput. Sci. Springer, London, 2001.
• P. Emanovský and J. K\"{u}hr. Some properties of pseudo-BCK- and pseudo-BCI-algebras. \emph{Fuzzy Sets and Systems}, \textbf{339}(2018), 1--16.
• A. Iampan. A new branch of the logical algebra: UP-algebras. J. Algebra Relat Top., 5(1)(2017), 35-–54.
• A. Iorgulescu. On pseudo-BCK algebras and porims. Sci. Math. Japonicae Online, 10(2004), 293-–305.
• A. Iorgulescu. Classes of pseudo-BCK algebras – Part I. J. of Mult.-Valued Logic Soft Comput., 12(2006), 71-–130.
• Y. B. Jun, M. Kondo and K. H. Kim. Pseudo-ideals of pseudo-BCK algebras. Sci. Math. Japonicae Online, 8(2003), 87--91.
• Y. B. Jun, H. S. Kim and J. Neggers. On pseudo-BCI ideals of pseudo-BCI algebras. Mat. Vesnik, 58(1)(2006), 39-–46.
• Y. B. Jun and A. Iampan. Shift UP-filters and decomposition of UP-filters in UP-Algebras. Missouri J. Math. Sci., 31(1)(2019), 36--45.
• K. J. Lee and C. H. Park. Some ideals of pseudo-BCI-algebras. J. Appl. Math. Inform., 27(1-2)(2009), 217-–231.
• D. A. Romano. Proper UP-filters in UP-algebra. Universal J. Math. Appl., 1(2)(2018), 98--100.
• D A. Romano. Notes on UP-ideals in UP-algebras. Comm. Advan. Math. Sci., 1(1)(2018), 35--38.
• D A. Romano. Some properties of proper UP-filters of UP-algebras. Fund. J. Math. Appl., 1(2)(2018), 109--111.
• D A. Romano. Some decomposition of UP-ideals and proper UP-filters. Math. Advan. Pure Appl. Sci., 2(1)(2019), 16--18.
• D. A. Romano. Pseudo-valuations on UP-algebras. Universal J. Math. Appl., 2(3)(2019), 138--140.
• D. A. Romano. Pseudo-UP algebras, An introduction. (To appear). Available at\\ https://www.researchgate.net/profile/DanielRomano
• J. Somjanta, N. Thuekaew, P. Kumpeangkeaw and A. Iampan. Fuzzy sets in UP-algebras. Ann. Fuzzy Math. Inform., 12(6)(2016), 739--756.
• A. Walendziak. On axiom systems of pseudo-BCK algebras. Bull. Malays. Math. Sci. Soc. (2), 34(2)(2011), 287-–293.