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Information Journal Paper

Title

CLASSICAL PRIME AND 2-ABSORBING L-SUBMODULES

Pages

  1-16

Abstract

 Let $L$ be a complete lattice. Let $R$ be a commutative ring, $M$ an $R$-module and $\nu$ an $L$-submodule of $M$. $\nu$ is called a classical prime $L$-submodule of $M$ if for any $L$-fuzzy points $a_r, b_s\in L^R$ and $x_t\in L^M$ ($a, b\in R$, $x\in M$ and $r, s, t\in L$), $a_rb_sx_t\in \nu$ implies that either $a_rx_t\in \nu$ or $b_sx_t\in \nu$. Assume that $\nu$ is an $L$-submodule of $mmu\in L(M)$. We say that $\nu$ is a $2$-absorbing $L$-submodule of $\mu$ if for any $L$-fuzzy points $a_r, b_s\in L^R$ and $x_t\in L^M$ ($a, b\in R$, $x\in M$ and $r, s, t\in L$), $a_rb_sx_t\in \nu$ implies that $a_rb_s\mu\subseteq \nu$ or $a_rx_t\in \nu$ or $b_sx_t\in \nu$. In this case every prime $L$-submodule of $M$ is a classical prime $L$-submodule, and every classical prime $L$-submodule is a $2$-absorbing $L$-submodule. In this paper we give some basic results concerning these classes of $L$-submodules. Finally we topologize $L-Cl. Spec(M)$, the set of all classical prime $L$-submodules of $M$, with Zariski topology.

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    APA: Copy

    YOUSEFIAN DARANI, a.. (2019). CLASSICAL PRIME AND 2-ABSORBING L-SUBMODULES. JOURNAL OF MATHEMATICAL EXTENSION, 13(2), 1-16. SID. https://sid.ir/paper/728480/en

    Vancouver: Copy

    YOUSEFIAN DARANI a.. CLASSICAL PRIME AND 2-ABSORBING L-SUBMODULES. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2019;13(2):1-16. Available from: https://sid.ir/paper/728480/en

    IEEE: Copy

    a. YOUSEFIAN DARANI, “CLASSICAL PRIME AND 2-ABSORBING L-SUBMODULES,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 13, no. 2, pp. 1–16, 2019, [Online]. Available: https://sid.ir/paper/728480/en

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