Yıl 2019, Cilt 48 , Sayı 5, Sayfalar 1454 - 1460 2019-10-08

On divided and regular divided rings

Chahrazade Bakkari [1]


In this paper, we study the notion of divided and regular divided rings. Then we establish the transfer of these notions to trivial ring extension and amalgamated algebras along an ideal. These results provide examples of non-divided regular divided rings. The article includes a brief discussion of the scope and precision of our results.
divided ring, regular divided ring, trivial ring extension, amalgamated algebras along an ideal
  • [1] K. Alaoui Ismaili and N. Mahdou, n-coherence property in amalgamated algebra along an ideal, Acta Math. Univ. Comenian. (N.S.), 86 (1), 59–72, 2017.
  • [2] A. Badawi, On divided commutative rings, Comm. Algebra, 27, 1465-1474, 1999.
  • [3] A. Badawi and D.E. Dobbs, On locally divided rings and going-down rings, Comm. Algebra, 29, 2805-2825, 2001.
  • [4] C. Bakkari, S. Kabbaj and N. Mahdou, Trivial extension defined by Prüfer condition, J. Pure Appl. Algebra, 214, 53–60, 2010.
  • [5] M. D’Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-canonical ideal, Ark. Mat. 45 (2), 241–252, 2007.
  • [6] M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl. 6 (3), 443–459, 2007.
  • [7] M. D’Anna, C.A. Finocchiaro and M. Fontana, Amalgamated algebras along an ideal, in: Commutative algebra and its applications, Walter de Gruyter, Berlin, 241–252, 2009.
  • [8] M. D’Anna, C.A Finocchiaro and M. Fontana, Properties of prime ideals in an amalgamated algebra along an ideal, J. Pure Appl. Algebra, 214, 1633–1641, 2010.
  • [9] M. D’Anna, C.A Finocchiaro and M. Fontana, Algebraic and topological properties of an amalgamated algebra along an ideal, Comm. Algebra, 44, 1836-1851, 2016.
  • [10] D.E. Dobbs, Divided rings and going-down, Pac. J. Math. 67 (2), 353-363, 1976.
  • [11] D.E. Dobbs and J. Shapiro, A generalization of divided domains and its connection to weak Baer going-down rings, Comm. Algebra, 37, 3553-3572, 2009.
  • [12] S. Glaz, Commutative Coherent Rings, Springer-Verlag, Lecture Notes in Mathe- matics, 1371, 1989.
  • [13] J.A. Huckaba, Commutative Rings with Zero Divizors, Marcel Dekker, New York Basel, 1988.
  • [14] S. Kabbaj and N. Mahdou, Trivial Extensions Defined by coherent-like condition, Comm. Algebra, 32 (10), 3937–3953, 2004.
  • [15] N. Mahdou and M.A. Moutui, fqp-property in amalgamated algebras along an ideal, Asian-Eur. J. Math. 8 (3), 2015.
  • [16] N. Mahdou, M. Chhiti and M. Tamekkante Clean property in Amalgamated algebras along an ideal, Hacet. J. Math. Stat. 44 (1), 41–49, 2015.
  • [17] N. Mahdou, A. Mimouni and M.A. Moutui, On almost valuation and almost Bézout rings, Comm. Algebra, 43, 297–308, 2015.
  • [18] H.R. Maimani and S. Yassemi, Zero-divisor graphs of amalgamated duplication of a ring along an ideal, J. Pure Appl. Algebra, 212 (1), 168–174, 2008.
  • [19] G. Picavet, Ideals and overring of divided domains, Int. Electron. J. Algebra, 8, 80–113, 2009.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0002-6387-7972
Yazar: Chahrazade Bakkari (Sorumlu Yazar)

Tarihler

Yayımlanma Tarihi : 8 Ekim 2019

Bibtex @araştırma makalesi { hujms629909, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1454 - 1460}, doi = {}, title = {On divided and regular divided rings}, key = {cite}, author = {Bakkari, Chahrazade} }
APA Bakkari, C . (2019). On divided and regular divided rings. Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1454-1460 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/49321/629909
MLA Bakkari, C . "On divided and regular divided rings". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1454-1460 <https://dergipark.org.tr/tr/pub/hujms/issue/49321/629909>
Chicago Bakkari, C . "On divided and regular divided rings". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1454-1460
RIS TY - JOUR T1 - On divided and regular divided rings AU - Chahrazade Bakkari Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1454 EP - 1460 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On divided and regular divided rings %A Chahrazade Bakkari %T On divided and regular divided rings %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U
ISNAD Bakkari, Chahrazade . "On divided and regular divided rings". Hacettepe Journal of Mathematics and Statistics 48 / 5 (Ekim 2019): 1454-1460 .
AMA Bakkari C . On divided and regular divided rings. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1454-1460.
Vancouver Bakkari C . On divided and regular divided rings. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1460-1454.