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Prime ideals of nearness semirings

Year 2019, Volume: 68 Issue: 2, 1867 - 1878, 01.08.2019
https://doi.org/10.31801/cfsuasmas.500382

Abstract

The aim of this paper is to introduced the concept of prime (semiprime) ideals of nearness semiring theory and give some properties of such ideals.

References

  • Biswas, R. and Nanda, S. Rough groups and rough subgroups, Bull. Pol. AC. Math, 42, (1994), 251-254.
  • Davvaz, B. Rough sets in a fundamental ring, Bull. Iranian Math. Soc, 24(2), (1998), 49-61.
  • Davvaz, B. Roughness in rings, Inform. Sci, 164(1-4), (2004), 147-163.
  • Golan, J. S. Semirings and Their Applications, Kluwer Academic Publishers, 1999.
  • İnan, E. and Öztürk, M. A. Near groups on nearness approximation spaces, Hacet. J. Math. Stat, 41(4), (2012), 545--558.
  • İnan, E. and Öztürk, M. A. Erratum and notes for near groups on nearness approximation spaces, Hacet. J. Math. Stat, 43(2), (2014), 279--281.
  • İnan, E. and Öztürk, M. A. Near semigroups on nearness approximation spaces, Ann. Fuzzy Math. Inform, 10(2), (2015), 287--297.
  • Iwinski, T. B. Algebraic approach to rough sets, Bull. Pol. AC. Math, 35, 1987, 673--683.
  • Kuroki, N. Rough ideals in semigroups, Inform. Sci, 100(1-4), (1997), 139--163.
  • Miao, D.; Han, S.; Li, D. and Sun, L. Rough group, rough subgroup and their properties, International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, Springer-Verlag, Heidelberg, 104-113, 2005.
  • Öztürk, M. A. and İnan, E. Soft nearness approximation spaces, Fund. Inform, 124(1), (2013), 231--250.
  • Öztürk, M. A.; Uçkun, M. and İnan, E. Near groups of weak cosets on nearness approximation spaces, Fund. Inform, 133, (2014), 433--448.
  • Öztürk, M. A.; Çelik Siner, İ. and Jun, Y. B. Nearness BCK-algebras, Int. J. Open Problems Compt. Math, 8(4), (2015) 37-57.
  • Öztürk, M. A. and İnan, E. Nearness rings, Ann. Fuzzy Math. Inform 2019, (In press).
  • Öztürk, M. A.; Jun, Y. B. and İz, A. Gamma semigroups on weak nearness approximation spaces, J. Int. Math. Virtual Inst, 9, (2019), 53-72.
  • Öztürk, M. A. Semiring on weak nearness approximation spaces, Ann. Fuzzy Math. Inform, 15(3), (2018), 227-241.
  • Pawlak, Z. Classification of objects by means of attributes, Institute for Computer Science, Polish Academy of Sciences, Report 429, 1981.
  • Pawlak, Z. Rough sets, Int. J. Comput. Inform. Sci, 11(5), (1982) 341-356.
  • Peters, J. F. Near sets: General theory about nearness of objects, Appl. Math. Sci, 1(53--56), (2007), 2609-2629.
  • Peters, J. F. Near sets: Special theory about nearness of objects, Fund. Inform, 75(1-4), (2007), 407--433.
  • Peters, J. F. Classification of perceptual objects by means of features, Int. J. Info. Technol. Intell. Comput, 3(2), (2008), 1-35.
  • Peters, J. F. Near sets: An introduction, Math. Comput. Sci, 7(1), (2013), 3--9.
  • Selvan, V. and Senthil Kumar, G. Rough ideals in semirings, Int. J. Math. Sci. Appl, 2(2), (2012), 557-564.
Year 2019, Volume: 68 Issue: 2, 1867 - 1878, 01.08.2019
https://doi.org/10.31801/cfsuasmas.500382

Abstract

References

  • Biswas, R. and Nanda, S. Rough groups and rough subgroups, Bull. Pol. AC. Math, 42, (1994), 251-254.
  • Davvaz, B. Rough sets in a fundamental ring, Bull. Iranian Math. Soc, 24(2), (1998), 49-61.
  • Davvaz, B. Roughness in rings, Inform. Sci, 164(1-4), (2004), 147-163.
  • Golan, J. S. Semirings and Their Applications, Kluwer Academic Publishers, 1999.
  • İnan, E. and Öztürk, M. A. Near groups on nearness approximation spaces, Hacet. J. Math. Stat, 41(4), (2012), 545--558.
  • İnan, E. and Öztürk, M. A. Erratum and notes for near groups on nearness approximation spaces, Hacet. J. Math. Stat, 43(2), (2014), 279--281.
  • İnan, E. and Öztürk, M. A. Near semigroups on nearness approximation spaces, Ann. Fuzzy Math. Inform, 10(2), (2015), 287--297.
  • Iwinski, T. B. Algebraic approach to rough sets, Bull. Pol. AC. Math, 35, 1987, 673--683.
  • Kuroki, N. Rough ideals in semigroups, Inform. Sci, 100(1-4), (1997), 139--163.
  • Miao, D.; Han, S.; Li, D. and Sun, L. Rough group, rough subgroup and their properties, International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, Springer-Verlag, Heidelberg, 104-113, 2005.
  • Öztürk, M. A. and İnan, E. Soft nearness approximation spaces, Fund. Inform, 124(1), (2013), 231--250.
  • Öztürk, M. A.; Uçkun, M. and İnan, E. Near groups of weak cosets on nearness approximation spaces, Fund. Inform, 133, (2014), 433--448.
  • Öztürk, M. A.; Çelik Siner, İ. and Jun, Y. B. Nearness BCK-algebras, Int. J. Open Problems Compt. Math, 8(4), (2015) 37-57.
  • Öztürk, M. A. and İnan, E. Nearness rings, Ann. Fuzzy Math. Inform 2019, (In press).
  • Öztürk, M. A.; Jun, Y. B. and İz, A. Gamma semigroups on weak nearness approximation spaces, J. Int. Math. Virtual Inst, 9, (2019), 53-72.
  • Öztürk, M. A. Semiring on weak nearness approximation spaces, Ann. Fuzzy Math. Inform, 15(3), (2018), 227-241.
  • Pawlak, Z. Classification of objects by means of attributes, Institute for Computer Science, Polish Academy of Sciences, Report 429, 1981.
  • Pawlak, Z. Rough sets, Int. J. Comput. Inform. Sci, 11(5), (1982) 341-356.
  • Peters, J. F. Near sets: General theory about nearness of objects, Appl. Math. Sci, 1(53--56), (2007), 2609-2629.
  • Peters, J. F. Near sets: Special theory about nearness of objects, Fund. Inform, 75(1-4), (2007), 407--433.
  • Peters, J. F. Classification of perceptual objects by means of features, Int. J. Info. Technol. Intell. Comput, 3(2), (2008), 1-35.
  • Peters, J. F. Near sets: An introduction, Math. Comput. Sci, 7(1), (2013), 3--9.
  • Selvan, V. and Senthil Kumar, G. Rough ideals in semirings, Int. J. Math. Sci. Appl, 2(2), (2012), 557-564.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Mehmet Ali Öztürk 0000-0002-1721-1053

İrfan Temur This is me 0000-0002-1846-2743

Publication Date August 1, 2019
Submission Date December 21, 2018
Acceptance Date January 23, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Öztürk, M. A., & Temur, İ. (2019). Prime ideals of nearness semirings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1867-1878. https://doi.org/10.31801/cfsuasmas.500382
AMA Öztürk MA, Temur İ. Prime ideals of nearness semirings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1867-1878. doi:10.31801/cfsuasmas.500382
Chicago Öztürk, Mehmet Ali, and İrfan Temur. “Prime Ideals of Nearness Semirings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1867-78. https://doi.org/10.31801/cfsuasmas.500382.
EndNote Öztürk MA, Temur İ (August 1, 2019) Prime ideals of nearness semirings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1867–1878.
IEEE M. A. Öztürk and İ. Temur, “Prime ideals of nearness semirings”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1867–1878, 2019, doi: 10.31801/cfsuasmas.500382.
ISNAD Öztürk, Mehmet Ali - Temur, İrfan. “Prime Ideals of Nearness Semirings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1867-1878. https://doi.org/10.31801/cfsuasmas.500382.
JAMA Öztürk MA, Temur İ. Prime ideals of nearness semirings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1867–1878.
MLA Öztürk, Mehmet Ali and İrfan Temur. “Prime Ideals of Nearness Semirings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1867-78, doi:10.31801/cfsuasmas.500382.
Vancouver Öztürk MA, Temur İ. Prime ideals of nearness semirings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1867-78.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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