On a class of $\lambda$ -modules
UDC 512.5 Smith in paper [{\it Mapping between module lattices}, Int. Electron. J. Algebra, {\bf 15}, 173–195 (2014)] introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an $R$-module $M,$ i.e., $\mu$ and $\lambda$ mappings. ...
Збережено в:
| Дата: | 2021 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2021
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/513 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 512.5
Smith in paper [{\it Mapping between module lattices}, Int. Electron. J. Algebra, {\bf 15}, 173–195 (2014)] introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an $R$-module $M,$ i.e., $\mu$ and $\lambda$ mappings. The definitions of the maps were motivated by the definition of multiplication modules. Moreover, some sufficient conditions for the maps to be a lattice homomorphisms are studied. In this work we define a class of $\lambda$-modules and observe the properties of the class. We give a sufficient conditions for the module and the ring such that the class $\lambda$ is a hereditary pretorsion class.
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| DOI: | 10.37863/umzh.v73i3.513 |