Research Article
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Year 2022, Volume: 3 Issue: 1, 46 - 56, 30.01.2022
https://doi.org/10.54974/fcmathsci.1032011

Abstract

References

  • Barnes W.E., On the Γ-rings of Nobusawa, Pacific Journal of Mathematics, 18, 411-422, 1966.
  • Clifford A., Preston G., The Algebraic Theory of Semigroups I. American Mathematical Society Mathematical Surveys. Providence, RI, USA: American Mathematical Society, 1961.
  • İnan E., Öztürk M.A., Near groups in nearness approximation spaces, Hacettepe Journal of Mathematics and Statistics, 41(4), 545-558, 2012.
  • İnan E., Öztürk M.A., Erratum and notes for near groups on nearness approximation spaces, Hacettepe Journal of Mathematics and Statistics, 43(2), 279-281, 2014.
  • İnan E., Öztürk M.A., Near semigroups on nearness approximation spaces, Annals of Fuzzy Mathematics and Informatics, 10(2), 287-297, 2015.
  • Kyuno S., On prime gamma rings, Pacific Journal of Mathematics, 75(1), 185-190, 1978.
  • Luh J., On the theory of simple Γ-rings, Michigan Mathematical Journal, 16, 65-75, 1969.
  • 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 Journal of Mathematics, 1, 81-89, 1964.
  • Öztürk M.A., İnan E., Nearness rings, Annals of Fuzzy Mathematics and Informatics, 17(2), 115-131, 2019.
  • Öztürk M.A., Uçkun M., İnan E., Near group of weak cosets on nearness approximation spaces, Fundamenta Informaticae, 133, 433-448, 2014.
  • Peters J.F., Near sets: General theory about nearness of objects, Applied Mathematical Sciences, 1(53-56), 2609-2629, 2007.
  • Peters J.F., Near sets: An introduction, Mathematics in Computer Science, 7(1), 3-9, 2013.
  • Peters J.F., Naimpally S.A., Applications of near sets, Notices of the American Mathematical Society, 59(4), 536-542, 2012.
  • Pilz G., Near-Rings: The Theory and Its Applications, North-Holland Publishing Company, 1983.
  • Satyanarayana B., A note on Γ-near-rings, Indian Journal of Mathematics, 41(3), 427-433, 1999.
  • Skowron A., Stepaniuk J., Tolerance approximation spaces, Fundamenta Informaticae, 27(2-3), 245- 253, 1996.
  • Uçkun M., Genç A., Near-rings on nearness approximation spaces, Turkish Journal of Mathematics, 45, 549-565, 2021.
  • Uçkun M., İnan E., Erol R., Nearness Γ-rings, Fundamentals of Contemporary Mathematical Sciences, 1(1), 37-48, 2020.
  • Wolski M., Perception and classification: A note on near sets and rough sets, Fundamenta Informaticae, 101(1-2), 143-155, 2010.
  • Zassenhaus H., Über endliche fastkörper, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 11, 187-220, 1935/1936.

Nearness Gamma-Near Rings

Year 2022, Volume: 3 Issue: 1, 46 - 56, 30.01.2022
https://doi.org/10.54974/fcmathsci.1032011

Abstract

The aim of this study is to introduce nearness Γ-near ring, nearness Γ-subnear ring and nearness Γ-ideal. Moreover, some properties of these structures are investigated.

References

  • Barnes W.E., On the Γ-rings of Nobusawa, Pacific Journal of Mathematics, 18, 411-422, 1966.
  • Clifford A., Preston G., The Algebraic Theory of Semigroups I. American Mathematical Society Mathematical Surveys. Providence, RI, USA: American Mathematical Society, 1961.
  • İnan E., Öztürk M.A., Near groups in nearness approximation spaces, Hacettepe Journal of Mathematics and Statistics, 41(4), 545-558, 2012.
  • İnan E., Öztürk M.A., Erratum and notes for near groups on nearness approximation spaces, Hacettepe Journal of Mathematics and Statistics, 43(2), 279-281, 2014.
  • İnan E., Öztürk M.A., Near semigroups on nearness approximation spaces, Annals of Fuzzy Mathematics and Informatics, 10(2), 287-297, 2015.
  • Kyuno S., On prime gamma rings, Pacific Journal of Mathematics, 75(1), 185-190, 1978.
  • Luh J., On the theory of simple Γ-rings, Michigan Mathematical Journal, 16, 65-75, 1969.
  • 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 Journal of Mathematics, 1, 81-89, 1964.
  • Öztürk M.A., İnan E., Nearness rings, Annals of Fuzzy Mathematics and Informatics, 17(2), 115-131, 2019.
  • Öztürk M.A., Uçkun M., İnan E., Near group of weak cosets on nearness approximation spaces, Fundamenta Informaticae, 133, 433-448, 2014.
  • Peters J.F., Near sets: General theory about nearness of objects, Applied Mathematical Sciences, 1(53-56), 2609-2629, 2007.
  • Peters J.F., Near sets: An introduction, Mathematics in Computer Science, 7(1), 3-9, 2013.
  • Peters J.F., Naimpally S.A., Applications of near sets, Notices of the American Mathematical Society, 59(4), 536-542, 2012.
  • Pilz G., Near-Rings: The Theory and Its Applications, North-Holland Publishing Company, 1983.
  • Satyanarayana B., A note on Γ-near-rings, Indian Journal of Mathematics, 41(3), 427-433, 1999.
  • Skowron A., Stepaniuk J., Tolerance approximation spaces, Fundamenta Informaticae, 27(2-3), 245- 253, 1996.
  • Uçkun M., Genç A., Near-rings on nearness approximation spaces, Turkish Journal of Mathematics, 45, 549-565, 2021.
  • Uçkun M., İnan E., Erol R., Nearness Γ-rings, Fundamentals of Contemporary Mathematical Sciences, 1(1), 37-48, 2020.
  • Wolski M., Perception and classification: A note on near sets and rough sets, Fundamenta Informaticae, 101(1-2), 143-155, 2010.
  • Zassenhaus H., Über endliche fastkörper, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 11, 187-220, 1935/1936.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Baki Çokakoğlu 0000-0002-7376-8526

Mustafa Uçkun 0000-0003-1813-5272

Publication Date January 30, 2022
Published in Issue Year 2022 Volume: 3 Issue: 1

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.