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.
[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).
[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).
İnan, E., & Kocamaz, A. (2022). Approximately Near Rings in Proximal Relator Spaces. Fundamental Journal of Mathematics and Applications, 5(4), 245-256. https://doi.org/10.33401/fujma.1117103
AMA
İnan E, Kocamaz A. Approximately Near Rings in Proximal Relator Spaces. Fundam. J. Math. Appl. December 2022;5(4):245-256. doi:10.33401/fujma.1117103
Chicago
İnan, Ebubekir, and Ayşegül Kocamaz. “Approximately Near Rings in Proximal Relator Spaces”. Fundamental Journal of Mathematics and Applications 5, no. 4 (December 2022): 245-56. https://doi.org/10.33401/fujma.1117103.
EndNote
İnan E, Kocamaz A (December 1, 2022) Approximately Near Rings in Proximal Relator Spaces. Fundamental Journal of Mathematics and Applications 5 4 245–256.
IEEE
E. İnan and A. Kocamaz, “Approximately Near Rings in Proximal Relator Spaces”, Fundam. J. Math. Appl., vol. 5, no. 4, pp. 245–256, 2022, doi: 10.33401/fujma.1117103.
ISNAD
İnan, Ebubekir - Kocamaz, Ayşegül. “Approximately Near Rings in Proximal Relator Spaces”. Fundamental Journal of Mathematics and Applications 5/4 (December 2022), 245-256. https://doi.org/10.33401/fujma.1117103.
JAMA
İnan E, Kocamaz A. Approximately Near Rings in Proximal Relator Spaces. Fundam. J. Math. Appl. 2022;5:245–256.
MLA
İnan, Ebubekir and Ayşegül Kocamaz. “Approximately Near Rings in Proximal Relator Spaces”. Fundamental Journal of Mathematics and Applications, vol. 5, no. 4, 2022, pp. 245-56, doi:10.33401/fujma.1117103.
Vancouver
İnan E, Kocamaz A. Approximately Near Rings in Proximal Relator Spaces. Fundam. J. Math. Appl. 2022;5(4):245-56.