Author:
Wijayanti I. E.,Ardiyansyah M. ,Prasetyo P. W.
Abstract
UDC 512.5Smith in paper [<em>Mapping between module lattices,</em> Int. Electron. J. Algebra, <strong>15</strong>, 173–195 (2014)] introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an -module i.e., and 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 -modules and observe the properties of the class. We give a sufficient conditions for the module and the ring such that the class is a hereditary pretorsion class.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Reference16 articles.
1. M. M. Ali, Invertibility of multiplication modules, New Zealand J. Math., 35, no. 1, 17 – 29 (2006).
2. M. M. Ali, Invertibility of multiplication modules. II, New Zealand J. Math., 39, 45 – 64 (2009).
3. M. Alkan, B. Sara¸c, Y. Tira¸s, Dedekind modules, Commun. Algebra, 33, 1617 – 1626 (2005), https://doi.org/10.1081/AGB-200061007
4. R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. and Math. Sci., 27, no. 27, 1715 – 1724 (2003), https://doi.org/10.1155/S0161171203202180
5. H. Ansari-Toroghy, F. Farshadifar, On multiplication and comultiplication modules, Acta Math. Sci. Ser. B., 31, № 2, 694 – 700 (2011), https://doi.org/10.1016/S0252-9602(11)60269-5