Prime ideals of nearness semirings

Yıl 2019, Cilt: 68 Sayı: 2, 1867 - 1878, 01.08.2019

Mehmet Ali Öztürk İrfan Temur

https://doi.org/10.31801/cfsuasmas.500382

Cited By: 7

Öz

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.

Anahtar Kelimeler

Semigroups, semirings, near sets, weak nearness approximation spaces, nearness semirings

Kaynakça

• 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.