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## MAPPINGS BETWEEN MODULE LATTICES

#### Patrick F. Smith [1]

##### 242 219

We examine the properties of certain mappings between the lattice of ideals of a commutative ring R and the lattice of submodules of an R-module M, in particular considering when these mappings are lattice homomorphisms. We prove that the mapping λ from the lattice of ideals of R to the lattice of submodules of M defined by λ(B) = BM for every ideal B of R is a (lattice) isomorphism if and only if M is a finitely generated faithful multiplication module. Moreover, for certain but not all rings R, there is an isomorphism from the lattice of ideals of R to the lattice of submodules of an R-module M if and only if the mapping λ is an isomorphism.
Lattice homomorphism, commutative ring, Prufer domain, multiplication module, Noetherian ring
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• Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland UK e-mail: Patrick.Smith@glasgow.ac.uk
Other ID JA72VD22VT Articles Author: Patrick F. Smith Publication Date: June 1, 2014
 Bibtex @ { ieja266246, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2014}, pages = {173 - 195}, doi = {10.24330/ieja.266246}, title = {MAPPINGS BETWEEN MODULE LATTICES}, key = {cite}, author = {Smith, Patrick F.} } APA Smith, P . (2014). MAPPINGS BETWEEN MODULE LATTICES. International Electronic Journal of Algebra, 15 (15), 173-195. DOI: 10.24330/ieja.266246 MLA Smith, P . "MAPPINGS BETWEEN MODULE LATTICES". International Electronic Journal of Algebra 15 (2014): 173-195 Chicago Smith, P . "MAPPINGS BETWEEN MODULE LATTICES". International Electronic Journal of Algebra 15 (2014): 173-195 RIS TY - JOUR T1 - MAPPINGS BETWEEN MODULE LATTICES AU - Patrick F. Smith Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266246 DO - 10.24330/ieja.266246 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 173 EP - 195 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266246 UR - https://doi.org/10.24330/ieja.266246 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra MAPPINGS BETWEEN MODULE LATTICES %A Patrick F. Smith %T MAPPINGS BETWEEN MODULE LATTICES %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266246 %U 10.24330/ieja.266246 ISNAD Smith, Patrick F. . "MAPPINGS BETWEEN MODULE LATTICES". International Electronic Journal of Algebra 15 / 15 (June 2014): 173-195. https://doi.org/10.24330/ieja.266246 AMA Smith P . MAPPINGS BETWEEN MODULE LATTICES. IEJA. 2014; 15(15): 173-195. Vancouver Smith P . MAPPINGS BETWEEN MODULE LATTICES. International Electronic Journal of Algebra. 2014; 15(15): 195-173.