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Let $R$ be a commutative ring with non-zero identity and let $NN(R)=\{I\,|\,I$ is a nonnil ideal of $R\}$. Let $M$ be an $R$-module and let $\phi$-$\rm{tor}(M)=\{x\in M\,|\,Ix=0$ for some $I\in NN(R)\}$. If $\phi$-$\rm{tor}(M)=M$, then $M$ is called a $\phi$-torsion module. An $R$-module $M$ is said to be $\phi$-flat, if $0\rightarrow A\otimes_RM\rightarrow B\otimes_RM\rightarrow C\otimes_RM\rightarrow 0$ is an exact $R$-sequence, for any exact sequence of $R$-modules $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$, where $C$ is $\phi$-torsion. In this paper, the concepts of NRD-submodules and NP-submodules are introduced, and the $\phi$-flat modules over a $\phi$-Prufer ring are investigated.
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참고문헌 (24)
참고문헌 신청
D. F. Anderson / 2004 / On ${\phi}$ -Prufer rings and ${\phi}$ -Bezout rings / Houston J. Math. 30(2):331~343
D. F. Anderson / 2005 / On ${\phi}$ -Dedekind rings and ${\phi}$ -Krull rings / Houston J. Math. 31(4):1007~1022
K. Bacem / 2016 / Nonnil-coherent rings / Beitr. Algebra Geom. 57(2):297~305
A. Badawi / 1999 / On divided commutative rings / Comm. Algebra 27(3):1465~1474
A. Badawi / 1999 / On ${\phi}$ -pseudo-valuation rings, in Advances in commutative ring theory (Fez, 1997), Lecture Notes in Pure and Appl. Math., 205 / Dekker :101~110
D. F. Anderson / 2005 / On
K. Bacem / 2016 / Nonnil-coherent rings / Beitr. Algebra Geom. 57(2):297~305
A. Badawi / 1999 / On divided commutative rings / Comm. Algebra 27(3):1465~1474
A. Badawi / 1999 / On
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