DOI: https://doi.org/10.14710/jfma.v5i2.15194

ROUGH RINGS, ROUGH SUBRINGS, AND ROUGH IDEALS

Fakhry Asad Agusfrianto  -  Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, Indonesia
*Fitriani Fitriani  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, Indonesia
Yudi Mahatma  -  Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, Indonesia

Citation Format:
Abstract

The basic concept in algebra that is set theory can be expanded into rough sets. Basic operations on the set such as intersections, unions, differences, and complements can still apply to rough sets. In addition, one of the applications of rough sets is the use of rough matrices in decision making. Furthermore, mathematical or informatics researchers who work on rough sets connect the concept of rough sets with algebraic structures (groups, rings, and modules) so that a concept called rough algebraic structures is obtained. Since the research related to rough sets is mostly carried out at the same time, different concepts have emerged related to rough sets and rough algebraic structures. In this paper, other definitions of rough ring and rough subring will be given along with related examples and theorems. Furthermore, it will also be defined the left ideal and the right ideal of the rough ring along with examples. Finally, we will discuss the theorem regarding rough ideals.

Fulltext View|Download

Article Metrics:

Article Info
Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
Recent articles
SYARAT PERLU DAN CUKUP ELEMEN NORMAL PADA RING DENGAN ELEMEN SATUAN RUANG BARISAN SELISIH DIPERUMUM TIPE CESARO PADA RUANG BERNORMA-N (CESARO GENERALIZED DIFFERENCE SEQUENCE SPACES ON N-NORMED SPACES) ANALISIS PERBANDINGAN METODE ARIMA DAN DOUBLE EXPONENTIAL SMOOTHING DARI BROWN PADA PERAMALAN INFLASI DI INDONESIA More recent articles
  1. Z. Pawlak, “Rough Sets,” Int. J. Comput. Inf. Sci., vol. 11, no. 5, pp. 341–356, 1982, doi: 10.1007/978-1-4613-1461-5_1
  2. B. Davvaz, “Roughness in rings,” Inf. Sci. (Ny)., vol. 164, no. 1–4, pp. 147–163, 2004, doi: 10.1016/j.ins.2003.10.001
  3. Q. F. Zhang, A. M. Fu, and S. X. Zhao, “Rough modules and their some properties,” Proc. 2006 Int. Conf. Mach. Learn. Cybern., vol. 2006, August, pp. 2290–2293, 2006, doi: 10.1109/ICMLC.2006.258675
  4. R. Radhamani and V. S. Selvi, “An Application of Soft Set and Fuzzy Set in Decision Making,” Int. J. Appl. Eng. Res., vol. 14, no. 3, pp. 75–78, 2019
  5. S. Vijayabalaji and P. Balaji, “Rough matrix theory and its decision making,” Int. J. Pure Appl. Math., vol. 87, no. 6, pp. 845–853, 2013, doi: 10.12732/ijpam.v87i6.13
  6. J. A. Gallian, Contemporary Abstract Algebra, Ninth Edition. CENGAGE Learning, 2017
  7. W. Adkins and S. H. Weintraub, Algebra : An Approach Via Module Theory. Baton Rouge: Springer-Verlag, 1992
  8. A. A. Nugraha, Fitriani, M. Ansori, and A. Faisol, “The Implementation of Rough Set on a Group Structure,” J. Mat. Mantik, vol. 8, no. 1, pp. 45–52, 2022, doi: 10.15642/mantik.2022.8.1.pp
  9. D. Miao, S. Han, D. Li, and L. Sun, “Rough Group , Rough Subgroup an Their Properties,” in Lecture Notes in Artificial Intelligence, no. 3641, 2005, pp. 104–113
  10. N. Bagirmaz and A. F. Ozcan, “Rough semigroups on approximation spaces,” Int. J. Algebr., vol. 9, no. 7, pp. 339–350, 2015, doi: 10.12988/ija.2015.5742
  11. A. K. Sinha and A. Prakash, “Rough exact sequences of modules,” Int. J. Appl. Eng. Res., vol. 11, no. 4, pp. 2513–2517, 2016
  12. B. Davvaz and M. Mahdavipour, “Roughness in modules,” Inf. Sci. (Ny)., vol. 176, no. 24, pp. 3658–3674, 2006, doi: 10.1016/j.ins.2006.02.014
  13. P. Isaac and U. Paul, “Rough G-modules and their properties,” Adv. Fuzzy Math., vol. 12, no. 1, pp. 93–100, 2017
  14. S. T. Almohammadi and C. ¨Ozel, “A New Approach to Rough Vector Spaces,” Gen. Lett. Math., vol. 6, no. 1, pp. 1–9, 2019, doi: 10.31559/glm2019.6.1.1
  15. S. Wahyuni, I. E. Wijayanti, D. A. Yuwaningsih, and A. D. Hartanto, Teori Ring dan Modul. Yogyakarta: Gadjah Mada University Press, 2016
  16. I. N. Herstein, Abstract Algebra, Third Edition. New Jersey: PRENTICE-HALL, 1996

Last update:

No citation recorded.

Last update:

No citation recorded.