Boole Yakın Halkalar ve Boole İdealler

Year 2018, Volume: 8 Issue: 1, 164 - 172, 31.01.2018

Funda Taşdemir , Melek Taş

https://doi.org/10.17714/gumusfenbil.334524

Abstract

Bu çalışmada, Boole
yakın halka kavramı yakın halkaların ideallerine genişletilerek Boole ideal
kavramı tanımlanmıştır. Elde edilen yeni tanımla birlikte Boole idealler ile
literatürdeki diğer yapılar arasındaki ilişkiler incelenmiştir. Her Boole
idealin aynı zamanda bir IFP ideal olduğu ancak tersinin doğru olmadığı
ispatlanmıştır. Yine, Boole yakın halkaların sıfırlayan ideallerinin de Boole
ideal olduğu ispatlanmıştır. Ayrıca, kendisi Boole olmadığı halde Boole ideale
sahip çeşitli yakın halkalar örnek olarak incelenmiştir. Son olarak, verilen
bir Boole halkadan Boole yakın halka elde etme yöntemi ile bir Boole yakın
halka elde edilmiştir.

Keywords

Boole ideal, Boole yakın halka, Yakın halka

Boolean Near Rings and Boolean Ideals

Abstract

In this paper, the concept of Boolean near ring
extended to ideals of near-rings, called Boolean ideals. With the obtained new
concept the relationships between Boolean ideals and the other concepts in the
literature have been examined. It has been proved that a Boolean ideal is also
an IFP ideal but the converse is not true. Also, it has been proved that
annihilator ideals of Boolean near-rings are Boolean ideals. Moreover it has
been examined that some examples to illustrate some near rings, which is not a
Boolean near-ring, but have Boolean ideals. Finally, a Boolean near ring has
been obtained from a given Boolean ring through the method of obtaining a
Boolean near ring.

Keywords

Boolean ideal, Boolean near ring, Near ring

References

• Atagün, A. O., 2010. IFP ideals in near-rings, Hacettepe Journal of Mathematics and Statistics, 39, 1, 17-21.
• Birkenmeier, G. ve Heatherly, H., 1989. Medial near-rings, Monatshefte für Mathematik, 107, 2, 89-110.
• Booth, G. L. ve Groenewald, N. J., 1996. ν-prime and ν-semiprime near-rings, Mathematica Japonica, 43, 3, 425-430.
• Booth, G. L., Groenewald, N. J. ve Veldsman, S., 1990. A Kurosh- Amitsur prime radical for near-rings, Communications in Algebra, 18, 9, 3111-3122.
• Clay, J. R. ve Lawyer, D. A., 1969. Boolean near-rings, Canadian Mathematical Bulletin, 12, 265-273.
• Dickson, L. E., 1905. Definitions of a group and a field by independent postulates, Transactions of the American Mathematical Society, 6, 2, 198-204.
• Groenewald, N. J., 1991. Different prime ideals in near-rings, Communications in Algebra, 19, 10, 2667-2675.
• Hansen, D. J. ve Luh, J., 1989. Boolean near-rings and weak commutativity, Journal of the Australian Mathematical Society Series A, 47, 103-107.
• Holcombe, W. L. M., 1970, Primitive Near-rings. PhD Thesis, University of Leeds. Leeds, 153p.
• Hungerford, T. W., 2003, Algebra, ed: S. Axler, F.W.Gehring, K.Ribet, Springer-Verlag, Newyork, 502p.
• Juglal, S., Groenewald, N. J. ve Lee, E. K. S., 2010. Different prime R-ideals, Algebra Colloquium, 17, 887-904.
• Pilz, G., 1983, Near-rings, North-Holland, Amsterdam, New York, Oxford, 470p.
• Ramakotaiah, D. ve Rao, G. K., 1979. IFP near-rings, Journal of Australian Mathematical Society, 27, 3, 365-370.
• Sezgin, A., Atagün, A. O. ve Aygün, E., 2011. A note on soft near-rings and idealistic soft near-rings, Filomat, 25, 1, 53-68.
• Taşdemir, F., Atagün, A. O. ve Altındiş, H., 2011. Equiprime N-ideals of monogenic N-groups, Hacettepe Journal of Mathematics and Statistics, 40, 3, 375-382.
• Taşdemir, F., Atagün, A. O. ve Altındiş, H., 2013. Different prime N-ideals and IFP N-ideals, Indian Journal of Pure and Applied Mathematics, 44, 4, 527-542.