Research Article
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Approximately gamma-rings in proximal relator spaces

Year 2019, Volume: 68 Issue: 2, 1780 - 1796, 01.08.2019
https://doi.org/10.31801/cfsuasmas.457040

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.

References

  • Barnes, W. E., On the Γ-rings of Nobusawa, Pacific J. Math., 18, (1966) 411-422.
  • Efremovič, V. A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N. S.) (Russian), 76, (1951) 341-343.
  • Efremovič, V. A., The geometry of proximity I, Mat. Sb. (N. S.) (Russian), 31(73) (1), (1952) 189-200.
  • İnan, E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (1), (2019) 572-582.
  • İnan, E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17, (2017) 479-487.
  • İnan, E., Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science, 8 (1), (2018) 24-41 .
  • Kovăr, M., A New Causal topology and why the universe is co-compact, arXiv:1112.0817 [math-ph], (2011) 1-15.
  • Kyuno, S., On prime gamma rings, Pacific J. Math., 75(1), (1978) 185-190.
  • Lodato, M., On Topologically Induced Generalized Proximity Relations, Ph.D. Thesis, Rutgers University, 1962.
  • Luh, J., On the theory of simple Γ-rings, Michigan Math. J., 16, (1969) 65-75.
  • Naimpally, S. A. and Peters, J. F., Topology with Applications: Topological Spaces via Near and Far, World Scientific, Singapore, 2013.
  • Nobusawa, N., On a generalization of the ring theory, Osaka J. Math., 1, (1964) 81-89.
  • Peters, J. F., Near Sets: An Introduction, Math. Comput. Sci., 7 (1), (2013) 3-9.
  • Peters, J. F. and Naimpally, S. A., Applications of near sets, Notices Amer. Math. Soc., 59 (4), (2012) 536-542.
  • Peters, J. F., Proximal relator spaces, Filomat, 30 (2), (2016) 469-472.
  • Peters, J. F., Öztürk, M. A. and Uçkun, M., Exactness of proximal groupoid homomorphisms, Adıyaman University Journal of Science, 5 (1), (2015) 1-13.
  • Peters, J. F., İnan, E. and Öztürk, M. A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes, 21 (2), (2014) 125-134.
  • Száz, Á., Basic tools and mild continuities in relator spaces, Acta Math. Hungar., 50 (3-4), (1987) 177-201.
Year 2019, Volume: 68 Issue: 2, 1780 - 1796, 01.08.2019
https://doi.org/10.31801/cfsuasmas.457040

Abstract

References

  • Barnes, W. E., On the Γ-rings of Nobusawa, Pacific J. Math., 18, (1966) 411-422.
  • Efremovič, V. A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N. S.) (Russian), 76, (1951) 341-343.
  • Efremovič, V. A., The geometry of proximity I, Mat. Sb. (N. S.) (Russian), 31(73) (1), (1952) 189-200.
  • İnan, E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (1), (2019) 572-582.
  • İnan, E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17, (2017) 479-487.
  • İnan, E., Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science, 8 (1), (2018) 24-41 .
  • Kovăr, M., A New Causal topology and why the universe is co-compact, arXiv:1112.0817 [math-ph], (2011) 1-15.
  • Kyuno, S., On prime gamma rings, Pacific J. Math., 75(1), (1978) 185-190.
  • Lodato, M., On Topologically Induced Generalized Proximity Relations, Ph.D. Thesis, Rutgers University, 1962.
  • Luh, J., On the theory of simple Γ-rings, Michigan Math. J., 16, (1969) 65-75.
  • Naimpally, S. A. and Peters, J. F., Topology with Applications: Topological Spaces via Near and Far, World Scientific, Singapore, 2013.
  • Nobusawa, N., On a generalization of the ring theory, Osaka J. Math., 1, (1964) 81-89.
  • Peters, J. F., Near Sets: An Introduction, Math. Comput. Sci., 7 (1), (2013) 3-9.
  • Peters, J. F. and Naimpally, S. A., Applications of near sets, Notices Amer. Math. Soc., 59 (4), (2012) 536-542.
  • Peters, J. F., Proximal relator spaces, Filomat, 30 (2), (2016) 469-472.
  • Peters, J. F., Öztürk, M. A. and Uçkun, M., Exactness of proximal groupoid homomorphisms, Adıyaman University Journal of Science, 5 (1), (2015) 1-13.
  • Peters, J. F., İnan, E. and Öztürk, M. A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes, 21 (2), (2014) 125-134.
  • Száz, Á., Basic tools and mild continuities in relator spaces, Acta Math. Hungar., 50 (3-4), (1987) 177-201.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Mustafa Uçkun 0000-0003-1813-5272

Publication Date August 1, 2019
Submission Date September 4, 2018
Acceptance Date November 26, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Uçkun, M. (2019). Approximately gamma-rings in proximal relator spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1780-1796. https://doi.org/10.31801/cfsuasmas.457040
AMA Uçkun M. Approximately gamma-rings in proximal relator spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1780-1796. doi:10.31801/cfsuasmas.457040
Chicago Uçkun, Mustafa. “Approximately Gamma-Rings in Proximal Relator Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1780-96. https://doi.org/10.31801/cfsuasmas.457040.
EndNote Uçkun M (August 1, 2019) Approximately gamma-rings in proximal relator spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1780–1796.
IEEE M. Uçkun, “Approximately gamma-rings in proximal relator spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1780–1796, 2019, doi: 10.31801/cfsuasmas.457040.
ISNAD Uçkun, Mustafa. “Approximately Gamma-Rings in Proximal Relator Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1780-1796. https://doi.org/10.31801/cfsuasmas.457040.
JAMA Uçkun M. Approximately gamma-rings in proximal relator spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1780–1796.
MLA Uçkun, Mustafa. “Approximately Gamma-Rings in Proximal Relator Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1780-96, doi:10.31801/cfsuasmas.457040.
Vancouver Uçkun M. Approximately gamma-rings in proximal relator spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1780-96.

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