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## MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES

#### Hosein Fazaeli Moghimi [1] , Javad Bagheri Harehdashti [2]

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Let R be a ring and R(M) be the lattice of radical submodules of an R-module M. Although the mapping ρ : R(R) → R(M) defined by ρ(I) = rad(IM) is a lattice homomorphism, the mapping σ : R(M) → R(R) defined by σ(N) = (N : M) is not necessarily so. In this paper, we examine the properties of σ, in particular considering when it is a homomorphism. We prove that a finitely generated R-module M is a multiplication module if and only if σ is a homomorphism. In particular, a finitely generated module M over a domain R is a faithful multiplication module if and only if σ is an isomorphism.
σ-modules, multiplication modules, primeful modules
Konular Matematik JA23FF48MF Makaleler Yazar: Hosein Fazaeli Moghimi Yazar: Javad Bagheri Harehdashti
 Bibtex @ { ieja266191, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {19}, pages = {35 - 48}, doi = {10.24330/ieja.266191}, title = {MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES}, key = {cite}, author = {Harehdashti, Javad Bagheri and Moghimi, Hosein Fazaeli} } APA Moghimi, H , Harehdashti, J . (2016). MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES. International Electronic Journal of Algebra, 19 (19), 35-48. DOI: 10.24330/ieja.266191 MLA Moghimi, H , Harehdashti, J . "MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES". International Electronic Journal of Algebra 19 (2016): 35-48 Chicago Moghimi, H , Harehdashti, J . "MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES". International Electronic Journal of Algebra 19 (2016): 35-48 RIS TY - JOUR T1 - MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES AU - Hosein Fazaeli Moghimi , Javad Bagheri Harehdashti Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266191 DO - 10.24330/ieja.266191 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 35 EP - 48 VL - 19 IS - 19 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266191 UR - http://dx.doi.org/10.24330/ieja.266191 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES %A Hosein Fazaeli Moghimi , Javad Bagheri Harehdashti %T MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 19 %N 19 %R doi: 10.24330/ieja.266191 %U 10.24330/ieja.266191 ISNAD Moghimi, Hosein Fazaeli , Harehdashti, Javad Bagheri . "MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES". International Electronic Journal of Algebra 19 / 19 (Haziran 2016): 35-48. http://dx.doi.org/10.24330/ieja.266191