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## Some results on relative dual Baer property

#### Tayyebeh AMOUZEGAR [1] , Rachid TRİBAK [2]

Let $R$ be a ring. In this article, we introduce and study relative dual Baer property. We characterize $R$-modules $M$ which are $R_R$-dual Baer, where $R$ is a commutative principal ideal domain. It is shown that over a right noetherian right hereditary ring $R$, an $R$-module $M$ is $N$-dual Baer for all $R$-modules $N$ if and only if $M$ is an injective $R$-module. It is also shown that for $R$-modules $M_1$, $M_2$, $\ldots$, $M_n$ such that $M_i$ is $M_j$-projective for all $i > j \in \{1,2,\ldots, n\}$, an $R$-module $N$ is $\bigoplus_{i=1}^nM_i$-dual Baer if and only if $N$ is $M_i$-dual Baer for all $i\in \{1,2,\ldots,n\}$. We prove that an $R$-module $M$ is dual Baer if and only if $S=End_R(M)$ is a Baer ring and $IM=r_M(l_S(IM))$ for every right ideal $I$ of $S$.
Baer rings, Dual Baer modules, Relative dual Baer property, Homomorphisms of modules
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Primary Language en Engineering Articles Orcid: 0000-0002-0600-5326Author: Tayyebeh AMOUZEGAR Institution: Quchan University of Advanced TechnologyCountry: Iran Orcid: 0000-0001-8400-4321Author: Rachid TRİBAK (Primary Author)Institution: Centre R\'{e}gional des M\'{e}tiers de l'Education et de la Formation (CRMEF-TTH)-Tanger, Avenue My Abdelaziz, SouaniCountry: Morocco Publication Date : September 6, 2020
 Bibtex @research article { jacodesmath790751, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {259 - 267}, doi = {10.13069/jacodesmath.790751}, title = {Some results on relative dual Baer property}, key = {cite}, author = {Amouzegar, Tayyebeh and Tri̇bak, Rachid} } APA Amouzegar, T , Tri̇bak, R . (2020). Some results on relative dual Baer property . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (3) , 259-267 . DOI: 10.13069/jacodesmath.790751 MLA Amouzegar, T , Tri̇bak, R . "Some results on relative dual Baer property" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 259-267 Chicago Amouzegar, T , Tri̇bak, R . "Some results on relative dual Baer property". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 259-267 RIS TY - JOUR T1 - Some results on relative dual Baer property AU - Tayyebeh Amouzegar , Rachid Tri̇bak Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.790751 DO - 10.13069/jacodesmath.790751 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 259 EP - 267 VL - 7 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.790751 UR - https://doi.org/10.13069/jacodesmath.790751 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Some results on relative dual Baer property %A Tayyebeh Amouzegar , Rachid Tri̇bak %T Some results on relative dual Baer property %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 3 %R doi: 10.13069/jacodesmath.790751 %U 10.13069/jacodesmath.790751 ISNAD Amouzegar, Tayyebeh , Tri̇bak, Rachid . "Some results on relative dual Baer property". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 3 (September 2020): 259-267 . https://doi.org/10.13069/jacodesmath.790751 AMA Amouzegar T , Tri̇bak R . Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(3): 259-267. Vancouver Amouzegar T , Tri̇bak R . Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(3): 259-267.

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