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MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES

Year 2016, , 35 - 48, 01.06.2016
https://doi.org/10.24330/ieja.266191

Abstract

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.

Year 2016, , 35 - 48, 01.06.2016
https://doi.org/10.24330/ieja.266191

Abstract

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Details

Subjects Mathematical Sciences
Other ID JA23FF48MF
Journal Section Articles
Authors

Hosein Fazaeli Moghimi This is me

Javad Bagheri Harehdashti This is me

Publication Date June 1, 2016
Published in Issue Year 2016

Cite

APA Moghimi, H. F., & Harehdashti, J. B. (2016). MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES. International Electronic Journal of Algebra, 19(19), 35-48. https://doi.org/10.24330/ieja.266191
AMA Moghimi HF, Harehdashti JB. MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES. IEJA. June 2016;19(19):35-48. doi:10.24330/ieja.266191
Chicago Moghimi, Hosein Fazaeli, and Javad Bagheri Harehdashti. “MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES”. International Electronic Journal of Algebra 19, no. 19 (June 2016): 35-48. https://doi.org/10.24330/ieja.266191.
EndNote Moghimi HF, Harehdashti JB (June 1, 2016) MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES. International Electronic Journal of Algebra 19 19 35–48.
IEEE H. F. Moghimi and J. B. Harehdashti, “MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES”, IEJA, vol. 19, no. 19, pp. 35–48, 2016, doi: 10.24330/ieja.266191.
ISNAD Moghimi, Hosein Fazaeli - Harehdashti, Javad Bagheri. “MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES”. International Electronic Journal of Algebra 19/19 (June 2016), 35-48. https://doi.org/10.24330/ieja.266191.
JAMA Moghimi HF, Harehdashti JB. MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES. IEJA. 2016;19:35–48.
MLA Moghimi, Hosein Fazaeli and Javad Bagheri Harehdashti. “MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES”. International Electronic Journal of Algebra, vol. 19, no. 19, 2016, pp. 35-48, doi:10.24330/ieja.266191.
Vancouver Moghimi HF, Harehdashti JB. MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES. IEJA. 2016;19(19):35-48.