Korean J. Math. Vol. 28 No. 1 (2020) pp.49-64
DOI: https://doi.org/10.11568/kjm.2020.28.1.49

Fuzzy prime spectrum of $C$-algebras

Article Sidebar

PDF
Published: Mar 30, 2020
Keywords:
C-algebras, fuzzy ideals, fuzzy prime ideals, fuzzy prime spectrum.
Mathematics Subject Classification:
03G05, 03G25, 03E72, 08A72

Main Article Content

Gezahagne Mulat Addis
Department of Mathematics University of Gondar Gondar, Ethiopia

Abstract

In this paper, we define fuzzy prime ideals of $ C- $algebras and investigate some of their properties. Furthermore, we study the topological properties of the space of fuzzy prime ideals of $ C- $algebra equipped with the hull-kernel topology.


Article Details

References

[1] B. A. Alaba and G. M. Addis, Fuzzy ideals of C−algebras, Intern. J. Fuzzy Mathematical Archive 16 (1) (2018), 21–31. Google Scholar

[2] B. A. Alaba and G. M. Addis, L−Fuzzy ideals in universal algebras, Ann. Fuzzy Math. Inform. 17 (1) (2019), 31–39. Google Scholar

[3] B. A. Alaba and G. M. Addis, L−Fuzzy prime ideals in universal algebras, Advances in Fuzzy Systems, vol. 2019, Article ID 5925036, 7 pages, 2019. Google Scholar

[4] B. A. Alaba and G. M. Addis, L−Fuzzy semi-prime ideals in universal algebras, Korean J. Math. 27 (2) (2019), 329–342. Google Scholar

[5] B. A. Alaba and G. M. Addis, Fuzzy congruence relations on almost distributive lattices, Ann. Fuzzy Math. Inform. 14 (3), (2017) 315–330. Google Scholar

[6] Y. Bo and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231–240. Google Scholar

[7] G. Birkhoof, Lattice theory, Amer. Math. Soc. Colloquium publications, Vol. 24 (1967). Google Scholar

[8] G. Gratzer, General lattice theory, Academic Press, New York(1978). Google Scholar

[9] F. Guzman and C. C. Squier, The algebra of conditional logic, Algebra Universalis 27 (1990), 88–110. Google Scholar

[10] A. K. Katsaras and D.B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl. 58 (1977), 135–146. Google Scholar

[11] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982) 133–139. Google Scholar

[12] G. C. Rao and P. Sundarayya, C-algebra as a poset, International Journal of Mathematical sciences 4 (2005), 225–236. Google Scholar

[13] G. C. Rao and P. Sundarayya, Decomposition of a C-algebra, Int. J. Math. Math. Sci. 2006, 1–8. Google Scholar

[14] A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512–517. Google Scholar

[15] U. M. Swamy, G. C. Rao and R. V. G. RaviKumar, Centre of a C-algebra, Southeast Asian Bulletin of Mathematics 27 (2003), 357–368. Google Scholar

[16] U. M. Swamy, G. C. Rao, P. Sundarayya and S. K. Vali, Semilattice structures on a C-algebra, Southeast Asian Bulletin of Mathematics 33 (2009), 551–561. Google Scholar

[17] U. M. Swamy and K. L. N. Swamy, Fuzzy prime ideals of rings, J. Math. Anal. Appl. 134 (1988), 94–103. Google Scholar

[18] S. K. Vali, P. Sundarayya and U. M. Swamy, Ideals of C-algebras, Asian-European Journal of Mathematics 3 (2010), 501–509 Google Scholar

[19] S. K. Vali, P. Sundarayya and U. M. Swamy, Ideal congruences on C-algebras, International Journal of Open Problems in Computer Science and Mathematics 3 (2010), 295–303 Google Scholar

[20] S. K. Vali and U. M. Swamy, Prime spectrum of a C-algebra, International Journal of Open Problems in Computer Science and Mathematics 4 (2011), 295–303. Google Scholar

[21] C. K. Wong, Fuzzy point and local properties of fuzzy topology, J. Math. Anal. Appl. 46 (l974), 316–328. Google Scholar

[22] L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338–353. Google Scholar