The singular ideal and the socle of incidence rings

Müge Kanuni Er; Özkay Özkan

doi:10.15672/hujms.684042

Araştırma Makalesi

Yıl 2021, Cilt: 50 Sayı: 2, 453 - 470, 11.04.2021

Müge Kanuni Er , Özkay Özkan

https://doi.org/10.15672/hujms.684042

Öz

Kaynakça

[1] F. Al-Thukair, S. Singh and I. Zaguia, Maximal ring of quotients of an incidence algebra, Arch. Math. 80, 358–362, 2003.
[2] S. Esin, M. Kanuni and A. Koç, Characterization of some ring properties in incidence algebras, Comm. Algebra, 39 (10), 3836–3848, 2011.
[3] M. Kanuni, Dense ideals and maximal quotient rings of incidence algebras, Comm. Algebra, 31 (11), 5287–5304, 2003.
[4] T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics 189, New York-Berlin, Springer-Verlag, 1999.
[5] E. Spiegel, Essential ideals of incidence algebras, J. Austral. Math. Soc. (Series A), 68, 252–260, 2000.
[6] E. Spiegel and C.J. O’Donnell, Incidence Algebras, Monographs and Textbooks in Pure Appl. Math. 206, New York, Marcel Dekker, 1997.

The singular ideal and the socle of incidence rings

Yıl 2021, Cilt: 50 Sayı: 2, 453 - 470, 11.04.2021

Müge Kanuni Er , Özkay Özkan

https://doi.org/10.15672/hujms.684042

Öz

Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.

Anahtar Kelimeler

incidence algebras, socle, singular ideal

Kaynakça

[1] F. Al-Thukair, S. Singh and I. Zaguia, Maximal ring of quotients of an incidence algebra, Arch. Math. 80, 358–362, 2003.
[2] S. Esin, M. Kanuni and A. Koç, Characterization of some ring properties in incidence algebras, Comm. Algebra, 39 (10), 3836–3848, 2011.
[3] M. Kanuni, Dense ideals and maximal quotient rings of incidence algebras, Comm. Algebra, 31 (11), 5287–5304, 2003.
[4] T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics 189, New York-Berlin, Springer-Verlag, 1999.
[5] E. Spiegel, Essential ideals of incidence algebras, J. Austral. Math. Soc. (Series A), 68, 252–260, 2000.
[6] E. Spiegel and C.J. O’Donnell, Incidence Algebras, Monographs and Textbooks in Pure Appl. Math. 206, New York, Marcel Dekker, 1997.

Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Müge Kanuni Er 0000-0001-7436-039X Özkay Özkan 0000-0001-6755-1497
Yayımlanma Tarihi	11 Nisan 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 50 Sayı: 2

Kaynak Göster

APA	Kanuni Er, M., & Özkan, Ö. (2021). The singular ideal and the socle of incidence rings. Hacettepe Journal of Mathematics and Statistics, 50(2), 453-470. https://doi.org/10.15672/hujms.684042
AMA	Kanuni Er M, Özkan Ö. The singular ideal and the socle of incidence rings. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):453-470. doi:10.15672/hujms.684042
Chicago	Kanuni Er, Müge, ve Özkay Özkan. “The Singular Ideal and the Socle of Incidence Rings”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 453-70. https://doi.org/10.15672/hujms.684042.
EndNote	Kanuni Er M, Özkan Ö (01 Nisan 2021) The singular ideal and the socle of incidence rings. Hacettepe Journal of Mathematics and Statistics 50 2 453–470.
IEEE	M. Kanuni Er ve Ö. Özkan, “The singular ideal and the socle of incidence rings”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 453–470, 2021, doi: 10.15672/hujms.684042.
ISNAD	Kanuni Er, Müge - Özkan, Özkay. “The Singular Ideal and the Socle of Incidence Rings”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 453-470. https://doi.org/10.15672/hujms.684042.
JAMA	Kanuni Er M, Özkan Ö. The singular ideal and the socle of incidence rings. Hacettepe Journal of Mathematics and Statistics. 2021;50:453–470.
MLA	Kanuni Er, Müge ve Özkay Özkan. “The Singular Ideal and the Socle of Incidence Rings”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 453-70, doi:10.15672/hujms.684042.
Vancouver	Kanuni Er M, Özkan Ö. The singular ideal and the socle of incidence rings. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):453-70.