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RISS 인기검색어
- 검색키워드
- 저자 : Shadi Asgari (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
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GENERALIZATIONS OF T-EXTENDING MODULES RELATIVE TO FULLY INVARIANT SUBMODULES
Asgari, Shadi,Haghany, Ahmad Korean Mathematical Society 2012 대한수학회지 Vol.49 No.3
The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.
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Generalizations of t-extending modules relative to fully invariant submodules
Shadi Asgari,Ahmad Haghany 대한수학회 2012 대한수학회지 Vol.49 No.3
The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.
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Injective property relative to nonsingular exact sequences
Marzieh Arabi-Kakavand,Shadi Asgari,Yaser Tolooei 대한수학회 2017 대한수학회보 Vol.54 No.2
We investigate modules $M$ having the injective property relative to nonsingular modules. Such modules are called ``$\mathcal N$-injective modules''. It is shown that $M$ is an $\mathcal N$-injective $R$-module if and only if the annihilator of $Z_2(R_R)$ in $M$ is equal to the annihilator of $Z_2(R_R)$ in $E(M)$. Every $\mathcal N$-injective $R$-module is injective precisely when $R$ is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal N$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) $R$-module is $\mathcal N$-injective, if and only if $R^{(\mathbb N)}$ is $\mathcal N$-injective, if and only if $R$ is right $t$-semisimple. The $\mathcal N$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal N$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.
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INJECTIVE PROPERTY RELATIVE TO NONSINGULAR EXACT SEQUENCES
Arabi-Kakavand, Marzieh,Asgari, Shadi,Tolooei, Yaser Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.
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