@article{Wijayanti_Ardiyansyah_Prasetyo_2021, title={On a class of $\lambda$ -modules}, volume={73}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/513}, DOI={10.37863/umzh.v73i3.513}, abstractNote={<p>UDC 512.5<br><br></p> <p>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.</p> <p><br><br><br></p>}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Wijayanti, I. E. and Ardiyansyah, M. and Prasetyo, P. W.}, year={2021}, month={Mar.}, pages={329 - 334} }