Quasi-dual Baer modules
نویسندگان
چکیده
Abstract Let R be a ring and let M an -module with $$S={\text {End}}_R(M)$$ S = End R ( M ) . The module is called quasi-dual Baer if for every fully invariant submodule N of , $$\{\phi \in S \mid Im\phi \subseteq N\} = eS$$ { ϕ ∈ ∣ I m ⊆ N } e some idempotent e in We show that only $$\sum _{\varphi \mathfrak {I}} \varphi (M)$$ ∑ φ direct summand left ideal $$\mathfrak {I}$$ $$R_R$$ finite product simple rings. Other characterizations modules are obtained. Examples which delineate the concepts results provided.
منابع مشابه
On quasi-baer modules
Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.
متن کاملon quasi-baer modules
let r be a ring, be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].
متن کاملBAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS
A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...
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ژورنال
عنوان ژورنال: Arabian Journal of Mathematics
سال: 2021
ISSN: ['2193-5343', '2193-5351']
DOI: https://doi.org/10.1007/s40065-021-00316-2