A Class of Abelian Rings

Sait Halicioglu; Abdullah Harmanci; Burcu Ungor

Published

2018-01-01

A Class of Abelian Rings

Una clase de anillos abelianos

Keywords:

Abelian ring, J-abelian ring, ring extension (en)
anillos abelianos, anillos J-abelianos, extensiones de anillos (es)

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Authors

Sait Halicioglu Ankara University
Abdullah Harmanci Hacettepe University
Burcu Ungor

Abstract (en)
Abstract (es)

Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-abelian if ae - ea ∈ J(R) for any a ∈ R and any idempotent e in R. In this paper, many characterizations of J-abelian rings are given. We prove that every J-Armendariz ring is J-abelian. We show that the class of J-abelian rings lies strictly between the class of abelian rings and the class of directly finite rings.

Sea R un anillo dotado de la identidad y sea J(R) el radical de Jacobson de R. Un anillo R se llama J-abeliano si ae - ea ∈ J(R) para todo a ∈ R y algún e idempotente en R. En este artículo, se dan muchas caracterizaciones de anillos J-abelianos. Demostramos que cada anillo J-Armendariz es J-abeliano. Mostramos que la clase de los anillos J-abelianos se ubica estrictamente entre la clase delos anillos abelianos y la clase de los anillos directamente finitos.

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How to Cite

APA

Halicioglu, S., Harmanci, A. and Ungor, B. (2018). A Class of Abelian Rings. Boletín de Matemáticas, 25(1), 27–37. https://revistas.unal.edu.co/index.php/bolma/article/view/79015

ACM

[1]

Halicioglu, S., Harmanci, A. and Ungor, B. 2018. A Class of Abelian Rings. Boletín de Matemáticas. 25, 1 (Jan. 2018), 27–37.

ACS

(1)

Halicioglu, S.; Harmanci, A.; Ungor, B. A Class of Abelian Rings. Bol. Matemáticas 2018, 25, 27-37.

ABNT

HALICIOGLU, S.; HARMANCI, A.; UNGOR, B. A Class of Abelian Rings. Boletín de Matemáticas, [S. l.], v. 25, n. 1, p. 27–37, 2018. Disponível em: https://revistas.unal.edu.co/index.php/bolma/article/view/79015. Acesso em: 22 jan. 2025.

Chicago

Halicioglu, Sait, Abdullah Harmanci, and Burcu Ungor. 2018. “A Class of Abelian Rings”. Boletín De Matemáticas 25 (1):27-37. https://revistas.unal.edu.co/index.php/bolma/article/view/79015.

Harvard

Halicioglu, S., Harmanci, A. and Ungor, B. (2018) “A Class of Abelian Rings”, Boletín de Matemáticas, 25(1), pp. 27–37. Available at: https://revistas.unal.edu.co/index.php/bolma/article/view/79015 (Accessed: 22 January 2025).

IEEE

[1]

S. Halicioglu, A. Harmanci, and B. Ungor, “A Class of Abelian Rings”, Bol. Matemáticas, vol. 25, no. 1, pp. 27–37, Jan. 2018.

MLA

Halicioglu, S., A. Harmanci, and B. Ungor. “A Class of Abelian Rings”. Boletín de Matemáticas, vol. 25, no. 1, Jan. 2018, pp. 27-37, https://revistas.unal.edu.co/index.php/bolma/article/view/79015.

Turabian

Halicioglu, Sait, Abdullah Harmanci, and Burcu Ungor. “A Class of Abelian Rings”. Boletín de Matemáticas 25, no. 1 (January 1, 2018): 27–37. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/bolma/article/view/79015.

Vancouver

1.

Halicioglu S, Harmanci A, Ungor B. A Class of Abelian Rings. Bol. Matemáticas [Internet]. 2018 Jan. 1 [cited 2025 Jan. 22];25(1):27-3. Available from: https://revistas.unal.edu.co/index.php/bolma/article/view/79015