TY  - JOUR
T1  - Some results on relative dual Baer property
AU  - Tribak, Rachid
AU  - Amouzegar, Tayyebeh
PY  - 2020
DA  - September
DO  - 10.13069/jacodesmath.790751
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 259
EP  - 267
VL  - 7
IS  - 3
LA  - en
AB  - 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 forall $R$-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 ringand $IM=r_M(l_S(IM))$ for every right ideal $I$ of $S$.
KW  - Baer rings
KW  - Dual Baer modules
KW  - Relative dual Baer property
KW  - Homomorphisms of modules
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UR  - https://doi.org/10.13069/jacodesmath.790751
L1  - https://dergipark.org.tr/en/download/article-file/1275018
ER  -