http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
- 中文 을 입력하시려면 zhongwen을 입력하시고 space를누르시면됩니다.
- 北京 을 입력하시려면 beijing을 입력하시고 space를 누르시면 됩니다.
RISS 인기검색어
- 검색키워드
- 저자 : Marzieh Arabi-Kakavand (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
-
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.
-
Modules whose classical prime submodules are intersections of maximal submodules
Marzieh Arabi-Kakavand,Mahmood Behboodi 대한수학회 2014 대한수학회보 Vol.51 No.1
Commutative rings in which every prime ideal is an inter- section of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that classical prime submodules are intersections of maximal submodules. It is shown that all co-semisimple modules as well as all Artinian modules are clas- sical Hilbert modules. Also, every module over a zero-dimensional ring is classical Hilbert. Results illustrating connections amongst the notions of classical Hilbert module and Hilbert ring are also provided. Rings R over which all modules are classical Hilbert are characterized. Further- more, we determine the Noetherian rings R for which all finitely generated R-modules are classical Hilbert.
-
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.
-
MODULES WHOSE CLASSICAL PRIME SUBMODULES ARE INTERSECTIONS OF MAXIMAL SUBMODULES
Arabi-Kakavand, Marzieh,Behboodi, Mahmood Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
Commutative rings in which every prime ideal is an intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that classical prime submodules are intersections of maximal submodules. It is shown that all co-semisimple modules as well as all Artinian modules are classical Hilbert modules. Also, every module over a zero-dimensional ring is classical Hilbert. Results illustrating connections amongst the notions of classical Hilbert module and Hilbert ring are also provided. Rings R over which all modules are classical Hilbert are characterized. Furthermore, we determine the Noetherian rings R for which all finitely generated R-modules are classical Hilbert.
연관 검색어 추천
이 검색어로 많이 본 자료
활용도 높은 자료
