Approximately Near Rings in Proximal Relator Spaces

Year 2022, Volume: 5 Issue: 4, 245 - 256, 01.12.2022

Ebubekir İnan , Ayşegül Kocamaz

https://doi.org/10.33401/fujma.1117103

Cited By: 1

Abstract

The motivation of this article is to define approximately near rings, some types of approximately near rings, approximately $N$-groups, approximately ideals, and approximately near rings of all descriptive approximately cosets. Moreover, some properties of these approximately algebraic structures are given. Furthermore, approximately near-ring homomorphisms are introduced and their some properties are investigated.

Keywords

Approximately ring, Descriptive approximation, Proximity space, Relator space

References

• [1] V. A. Efremovi˘c, The geometry of proximity I., Mat. Sb. (N.S.), 31 73(1) (1952), 189-200.
• [2] M. Lodato, On Topologically Induced Generalized Proximity Relations, Ph.D. Thesis, Rutgers University 1962.
• [3] J. F. Peters, Proximal relator spaces, Filomat, 30 (2) (2019), 469-472.
• [4] E. İnan, Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (1) (2019), 572-582.
• [5] E. İnan, Approximately semigroups and ideals: An algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17 (2017), 479-487.
• [6] E. İnan, Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science, 8 (1) (2018), 24-41.
• [7] E. İnan, Approximately rings in proximal relator spaces, Turkish J. Math., 43 (2019) 2941-2953.
• [8] E. İnan, M. Uçkun, Approximately G-semigroups in proximal relator spaces, Appl. Algebra Engrg. Comm. Comput., 30 (4) (2019), 299-311.
• [9] G. Pilz, Near-Rings: The Theory and Its Applications, 2nd Ed., North-Holland Publishing Company, Amsterdam, 1983.
• [10] J. F. Peters, Near sets: An introduction, Math. Comput. Sci., 7 (1) (2013), 3-9.
• [11] J. F. Peters, E. inan , M. A. Öztürk, Spatial and descriptive isometries in proximity spaces, General Mathematics Notes, 21 (2) (2014), 1-10.
• [12] M. Kov˘ar, A new causal topology and why the universe is co-compact, (2011), 1-15, arXiv:1112.0817 [math-ph].
• [13] S. A. Naimpally, J. F. Peters, Topology with Applications: Topological Spaces via Near and Far, World Scientific, Singapore, 2013.
• [14] J. F. Peters, M. A. O¨ ztu¨rk, M. Uc¸kun, Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science, 5 (1) (2015), 1-13.
• [15] A. Clifford, G. Preston, The Algebraic Theory of Semigroups I, Amer. Math. Soc., Providence, RI, Mathematical Surveys (1961).