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Approximately Gamma-Near Rings

Year 2024, Volume: 16 Issue: 1, 6 - 15, 30.06.2024
https://doi.org/10.47000/tjmcs.938957

Abstract

The focus of this work is to introduce approximately gamma-near ring, approximately gamma-ideal and approximately
gamma-near ring of all descriptive approximately cosets. Also, some properties of approximately gamma-near ring and
approximately gamma-ideal were given.

References

  • Barnes, W.E., On the Γ-rings of Nobusawa, Pacific J. Math., 18(1966), 411–422.
  • Efremovic, V.A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N.S.) (Russian), 76(1951), 341–343.
  • Efremovic, V.A., The geometry of proximity I, Mat. Sb. (N.S.) (Russian), 31(73)(1)(1952), 189–200.
  • 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.
  • İnan, E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1)(2019), 572–582.
  • İnan, E., Uçkun, M., Approximately Γ-semigroups in proximal relator spaces, Applicable Algebra in Engineering Communication and Computing,30(4)(2019), 299–311.
  • İnan, E., Approximately rings in proximal relator spaces, Turkish Journal of Mathematics, 43(6)(2019), 2941–2953.
  • İnan, E., Kocamaz, A., Approximately near rings in proximal relator spaces, Fundamental Journal of Mathematics and Applications, 5(4)(2022), 245–256.
  • Kovar, 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.
  • Luh, J., On the theory of simple Γ-rings, Michigan Math. J., 16(1969), 65–75.
  • Naimpally, S.A., Peters, J.F., Topology with Applications: Topological Spaces via Near and Far, World Scientific, 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., 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., Uçkun, M., Exactness of proximal groupoid homomorphisms, Adıyaman University Journal of Science, 5(1)(2015), 1–13.
  • Peters, J.F., İnan, E., Öztürk, M.A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes, 21(2)(2014), 125–134.
  • Pilz, G., Near-Rings: The Theory and Its Applications, 2nd Ed., North-Holland Publishing Company, 1983.
  • Satyanarayana, B., A note on Γ-near-rings, Indian J. Math., 41(3)(1999), 427–433.
  • Szaz, A., Basic tools and mild continuities in relator spaces, Acta Math. Hungar., 50(3-4)(1987), 177–201.
  • Uçkun, M., Approximately Γ-rings in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2)(2019), 1780–1796.
Year 2024, Volume: 16 Issue: 1, 6 - 15, 30.06.2024
https://doi.org/10.47000/tjmcs.938957

Abstract

References

  • Barnes, W.E., On the Γ-rings of Nobusawa, Pacific J. Math., 18(1966), 411–422.
  • Efremovic, V.A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N.S.) (Russian), 76(1951), 341–343.
  • Efremovic, V.A., The geometry of proximity I, Mat. Sb. (N.S.) (Russian), 31(73)(1)(1952), 189–200.
  • 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.
  • İnan, E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1)(2019), 572–582.
  • İnan, E., Uçkun, M., Approximately Γ-semigroups in proximal relator spaces, Applicable Algebra in Engineering Communication and Computing,30(4)(2019), 299–311.
  • İnan, E., Approximately rings in proximal relator spaces, Turkish Journal of Mathematics, 43(6)(2019), 2941–2953.
  • İnan, E., Kocamaz, A., Approximately near rings in proximal relator spaces, Fundamental Journal of Mathematics and Applications, 5(4)(2022), 245–256.
  • Kovar, 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.
  • Luh, J., On the theory of simple Γ-rings, Michigan Math. J., 16(1969), 65–75.
  • Naimpally, S.A., Peters, J.F., Topology with Applications: Topological Spaces via Near and Far, World Scientific, 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., 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., Uçkun, M., Exactness of proximal groupoid homomorphisms, Adıyaman University Journal of Science, 5(1)(2015), 1–13.
  • Peters, J.F., İnan, E., Öztürk, M.A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes, 21(2)(2014), 125–134.
  • Pilz, G., Near-Rings: The Theory and Its Applications, 2nd Ed., North-Holland Publishing Company, 1983.
  • Satyanarayana, B., A note on Γ-near-rings, Indian J. Math., 41(3)(1999), 427–433.
  • Szaz, A., Basic tools and mild continuities in relator spaces, Acta Math. Hungar., 50(3-4)(1987), 177–201.
  • Uçkun, M., Approximately Γ-rings in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2)(2019), 1780–1796.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mustafa Uçkun 0000-0003-1813-5272

Mehmet Gürbüzcan This is me 0000-0003-1007-1016

Publication Date June 30, 2024
Published in Issue Year 2024 Volume: 16 Issue: 1

Cite

APA Uçkun, M., & Gürbüzcan, M. (2024). Approximately Gamma-Near Rings. Turkish Journal of Mathematics and Computer Science, 16(1), 6-15. https://doi.org/10.47000/tjmcs.938957
AMA Uçkun M, Gürbüzcan M. Approximately Gamma-Near Rings. TJMCS. June 2024;16(1):6-15. doi:10.47000/tjmcs.938957
Chicago Uçkun, Mustafa, and Mehmet Gürbüzcan. “Approximately Gamma-Near Rings”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 6-15. https://doi.org/10.47000/tjmcs.938957.
EndNote Uçkun M, Gürbüzcan M (June 1, 2024) Approximately Gamma-Near Rings. Turkish Journal of Mathematics and Computer Science 16 1 6–15.
IEEE M. Uçkun and M. Gürbüzcan, “Approximately Gamma-Near Rings”, TJMCS, vol. 16, no. 1, pp. 6–15, 2024, doi: 10.47000/tjmcs.938957.
ISNAD Uçkun, Mustafa - Gürbüzcan, Mehmet. “Approximately Gamma-Near Rings”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 6-15. https://doi.org/10.47000/tjmcs.938957.
JAMA Uçkun M, Gürbüzcan M. Approximately Gamma-Near Rings. TJMCS. 2024;16:6–15.
MLA Uçkun, Mustafa and Mehmet Gürbüzcan. “Approximately Gamma-Near Rings”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 6-15, doi:10.47000/tjmcs.938957.
Vancouver Uçkun M, Gürbüzcan M. Approximately Gamma-Near Rings. TJMCS. 2024;16(1):6-15.