Approximately gamma-rings in proximal relator spaces

Abstract

This article introduces approximately gamma-rings, approximately gamma-

ideals and approximately gamma-rings of all descriptive approximately cosets by

considering new operations on the set of all descriptive approximately cosets.

Afterwards, some properties of approximately gamma-rings and gamma-ideals were given.

Keywords

• Proximity spaces,relator spaces,descriptive approximations,approximately gamma-rings

References

1. Barnes, W. E., On the Γ-rings of Nobusawa, Pacific J. Math., 18, (1966) 411-422.
2. Efremovič, V. A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N. S.) (Russian), 76, (1951) 341-343.
3. Efremovič, V. A., The geometry of proximity I, Mat. Sb. (N. S.) (Russian), 31(73) (1), (1952) 189-200.
4. İnan, E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (1), (2019) 572-582.
5. İnan, E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17, (2017) 479-487.
6. İnan, E., Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science, 8 (1), (2018) 24-41 .
7. Kovăr, M., A New Causal topology and why the universe is co-compact, arXiv:1112.0817 [math-ph], (2011) 1-15.
8. Kyuno, S., On prime gamma rings, Pacific J. Math., 75(1), (1978) 185-190.

9. Lodato, M., On Topologically Induced Generalized Proximity Relations, Ph.D. Thesis, Rutgers University, 1962.
10. Luh, J., On the theory of simple Γ-rings, Michigan Math. J., 16, (1969) 65-75.
11. Naimpally, S. A. and Peters, J. F., Topology with Applications: Topological Spaces via Near and Far, World Scientific, Singapore, 2013.
12. Nobusawa, N., On a generalization of the ring theory, Osaka J. Math., 1, (1964) 81-89.
13. Peters, J. F., Near Sets: An Introduction, Math. Comput. Sci., 7 (1), (2013) 3-9.
14. Peters, J. F. and Naimpally, S. A., Applications of near sets, Notices Amer. Math. Soc., 59 (4), (2012) 536-542.
15. Peters, J. F., Proximal relator spaces, Filomat, 30 (2), (2016) 469-472.
16. Peters, J. F., Öztürk, M. A. and Uçkun, M., Exactness of proximal groupoid homomorphisms, Adıyaman University Journal of Science, 5 (1), (2015) 1-13.
17. Peters, J. F., İnan, E. and Öztürk, M. A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes, 21 (2), (2014) 125-134.
18. Száz, Á., Basic tools and mild continuities in relator spaces, Acta Math. Hungar., 50 (3-4), (1987) 177-201.