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Değişmeli Halkalarda n-ideallerin Genelleştirmeleri

Yıl 2019, Cilt: 12 Sayı: 2, 650 - 657, 31.08.2019
https://doi.org/10.18185/erzifbed.471609

Öz

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.

Kaynakça

  • 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.

Generalizations of n-ideals of Commutative Rings

Yıl 2019, Cilt: 12 Sayı: 2, 650 - 657, 31.08.2019
https://doi.org/10.18185/erzifbed.471609

Öz


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.

Kaynakça

  • 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.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Ece Yetkin Çelikel 0000-0001-6194-656X

Yayımlanma Tarihi 31 Ağustos 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 2

Kaynak Göster

APA Yetkin Çelikel, E. (2019). Generalizations of n-ideals of Commutative Rings. Erzincan University Journal of Science and Technology, 12(2), 650-657. https://doi.org/10.18185/erzifbed.471609

Cited By

S-n-ideals of commutative rings
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1099300