IJPAM: Volume 116, No. 2 (2017)

Title

WHEN THE MAPPING CARRYING SUBMODULES TO
THEIR RADICALS IS A LATTICE HOMOMORPHISM

Authors

Javad Bagheri Harehdashti$^1$, Hosein Fazaeli Moghimi$^2$
$^{1,2}$Department of Mathematics
University of Birjand
Birjand, IRAN

Abstract

Let $R$ be a commutative ring and $M$ be a unital $R$-module. In this paper, we investigate when the mapping $\eta_M:\mathcal{L}(M)\rightarrow \lrm$, from the lattice of submodules of $M$ to the lattice of radical submodules of $M$ defined by $\eta_M(N)=\rad N$ is a lattice homomorphism. We show that if $M$ is an $R$-module which satisfies the radical formula, then $\eta_M$ is a lattice homomorphism if and only if $\rad(L\cap N)=\rad L \cap \rad N,$ for all finitely generated submodules $L$ and $N$ of $M$.

History

Received: 2017-01-28
Revised: 2017-06-01
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 13C13, 06B99, 13C99
Key Words and Phrases: radical of submodule, multiplication module, $\eta$-module

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How to Cite?

DOI: 10.12732/ijpam.v116i2.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 353 - 360


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