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WINTER 2015 Anti-homomorphisms between module lattices
Patrick F. Smith
J. Commut. Algebra 7(4): 567-592 (WINTER 2015). DOI: 10.1216/JCA-2015-7-4-567

Abstract

We examine the properties of certain mappings between the lattice $\mathcal{L}(R)$ of ideals of a commutative ring $R$ and the lattice $\mathcal{L}(_RM)$ of submodules of an $R$-module $M$, in particular considering when these mappings are lattice anti-homomorphisms. The mappings in question are the mapping $\alpha : \mathcal{L}(R) \rightarrow \mathcal{L}(_RM)$ defined by setting for each ideal $B$ of $R$, $\alpha(B)$ to be the submodule of $M$ consisting of all elements $m$ in $M$ with $Bm = 0$ and the mapping $\beta : \mathcal{L}(_RM) \rightarrow \mathcal{L}(R)$ defined by $\beta(N)$ is the annihilator in $R$ of $N$, for each submodule $N$ of $M$.

Citation

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Patrick F. Smith. "Anti-homomorphisms between module lattices." J. Commut. Algebra 7 (4) 567 - 592, WINTER 2015. https://doi.org/10.1216/JCA-2015-7-4-567

Information

Published: WINTER 2015
First available in Project Euclid: 19 January 2016

zbMATH: 1341.13006
MathSciNet: MR3451356
Digital Object Identifier: 10.1216/JCA-2015-7-4-567

Subjects:
Primary: 06A30, 13A15, 13C12, 13C99, 13F05

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.7 • No. 4 • WINTER 2015
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