Year 2020, Volume 49 , Issue 1, Pages 371 - 379 2020-02-06

Some commutative ring extensions defined by almost Bézout condition

Najib Ouled AZAİEZ [1] , Moutu ABDOU SALAM MOUTUİ [2]


In this paper, we study the almost Bézout property in different commutative ring extensions, namely, in bi-amalgamated algebras and pairs of rings. In Section 2, we deal with almost Bézout domains issued from bi-amalgamations. Our results capitalize well known results on amalgamations and pullbacks as well as generate new original class of rings satisfying this property. Section 3 investigates pairs of rings where all intermediate rings are almost Bézout domains. As an application of our results, we characterize pairs of rings $(R,T)$, where $R$ arises from a $(T,M,D)$ construction to be an almost Bézout domain.
Bi-amalgamated algebra, almost Bézout domain, pairs of rings, pullbacks
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-0082-4611
Author: Najib Ouled AZAİEZ
Institution: King Faisal University
Country: Saudi Arabia


Orcid: 0000-0002-7544-2749
Author: Moutu ABDOU SALAM MOUTUİ (Primary Author)
Institution: King Faisal University
Country: Saudi Arabia


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms552224, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {371 - 379}, doi = {10.15672/hujms.552224}, title = {Some commutative ring extensions defined by almost Bézout condition}, key = {cite}, author = {AZAİEZ, Najib Ouled and ABDOU SALAM MOUTUİ, Moutu} }
APA AZAİEZ, N , ABDOU SALAM MOUTUİ, M . (2020). Some commutative ring extensions defined by almost Bézout condition. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 371-379 . DOI: 10.15672/hujms.552224
MLA AZAİEZ, N , ABDOU SALAM MOUTUİ, M . "Some commutative ring extensions defined by almost Bézout condition". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 371-379 <https://dergipark.org.tr/en/pub/hujms/issue/52287/552224>
Chicago AZAİEZ, N , ABDOU SALAM MOUTUİ, M . "Some commutative ring extensions defined by almost Bézout condition". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 371-379
RIS TY - JOUR T1 - Some commutative ring extensions defined by almost Bézout condition AU - Najib Ouled AZAİEZ , Moutu ABDOU SALAM MOUTUİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.552224 DO - 10.15672/hujms.552224 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 371 EP - 379 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.552224 UR - https://doi.org/10.15672/hujms.552224 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Some commutative ring extensions defined by almost Bézout condition %A Najib Ouled AZAİEZ , Moutu ABDOU SALAM MOUTUİ %T Some commutative ring extensions defined by almost Bézout condition %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.552224 %U 10.15672/hujms.552224
ISNAD AZAİEZ, Najib Ouled , ABDOU SALAM MOUTUİ, Moutu . "Some commutative ring extensions defined by almost Bézout condition". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 371-379 . https://doi.org/10.15672/hujms.552224
AMA AZAİEZ N , ABDOU SALAM MOUTUİ M . Some commutative ring extensions defined by almost Bézout condition. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 371-379.
Vancouver AZAİEZ N , ABDOU SALAM MOUTUİ M . Some commutative ring extensions defined by almost Bézout condition. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 379-371.