Prime ideals of nearness semirings
Year 2019,
Volume: 68 Issue: 2, 1867 - 1878, 01.08.2019
Mehmet Ali Öztürk
,
İrfan Temur
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
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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.
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Davvaz, B. Roughness in rings, Inform. Sci, 164(1-4), (2004), 147-163.
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Golan, J. S. Semirings and Their Applications, Kluwer Academic Publishers, 1999.
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İnan, E. and Öztürk, M. A. Near groups on nearness approximation spaces, Hacet. J. Math. Stat, 41(4), (2012), 545--558.
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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.
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İnan, E. and Öztürk, M. A. Near semigroups on nearness approximation spaces, Ann. Fuzzy Math. Inform, 10(2), (2015), 287--297.
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Iwinski, T. B. Algebraic approach to rough sets, Bull. Pol. AC. Math, 35, 1987, 673--683.
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Kuroki, N. Rough ideals in semigroups, Inform. Sci, 100(1-4), (1997), 139--163.
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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.
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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
Mehmet Ali Öztürk
,
İrfan Temur
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.