Değişmeli Halkalarda n-ideallerin Genelleştirmeleri

R değişmeli, birimli bir halka olsun ve, nin tüm ideallerinin kümesini göstersin. Bu çalışmada, esas olarak değişmeli halkalarda ideal kavramının bir fonksiyonu aracıyla genelleştirmeleri üzerinde duracağız. Bu ideal sınıfının özellikleri detaylarıyla incelenecektir.

Anahtar Kelimeler:

n-ideal, phi-n-ideal, phi-asal ideal, phi-asalımsı ideal

Generalizations of n-ideals of Commutative Rings

Let be a commutative ring with identity and denotes the set of all ideals of . We will concerned in this study mainly with the generalizations of -ideals in commutative rings via a function . Properties of this class of ideals will investigated in detail.

Keywords:

n-ideal, phi-n-ideal, phi-prime ideal, phi-primary ideal,

PDF

___

Anderson D. D. and Batanieh, M., 2008. “Generalizations of prime ideals”, Communications in Algebra, 36, 686-696.
Anderson D. D. and Smith, E., 2003. “Weakly prime ideals”, Houston Journal of Mathematics, 29, 831-840.
Anderson D. F. and Badawi, A., 2011. “On n-absorbing ideals of commutative rings”, Communications in Algebra, 39, 1646-1672.
Atani, E. S. and Farzalipour, F. 2005. “On weakly primary ideals”, Georgian Mathematical Journal”, 12, 423–429.
Badawi, A., 2007. “On 2-absorbing ideals of commutative rings”, Bulletin of the Australian Mathematical Society, 75, 417-429.
Badawi, A., Tekir U. and Yetkin Çelikel, E., 2014. “On 2-absorbing primary ideals in commutative rings”, Bulletin of the Korean Mathematical Society, 51 (4) 1163-1173.
Badawi, A., Tekir U. and Yetkin Çelikel, E., 2014. “On weakly 2-absorbing primary ideals of commutative rings”, Journal of the Korean Mathematical Society, 52 (1), 97–111.
Badawi, A., Tekir, Un, Aslankarayiğit Uğurlu, E., Ulucak, G., Yetkin Çelikel, E., 2016. “Generalizations of 2-absorbing primary ideals of commutative rings”, Turkish Journal of Mathematics, 40, 703 – 717.
Badawi, A., Darani, A.Y, 2013. “On weakly 2-absorbing ideals of commutative rings”, Houston Journal of Mathematics, 39, 441–452.
Batanieh, M., 2006. “Generalization of prime ideals”. PhD Thesis, The University of Iowa, 1-37.
Darani, A.Y., 2012. “Generalizations of primary ideals in commutative rings”, Novi Sad Journal of Mathematics, 42 (1), 27-32.
Huckaba, J., (1988). “Commutative rings with zero divisors”, Marcel Dekker, Inc., New York.
Khaksari, A., 2015. “φ-2-absorbing ideals”, International Journal of Pure and Applied Mathematics, 99 (1), 1-10.
Tekir, U., Koc, S., Oral, K.H., 2017. “n-ideals of commutative rings”, Filomat, 31 (10), 2933-2941.