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- Title
ON THE DISTRIBUTIVITY OF THE LATTICE OF RADICAL SUBMODULES.
- Authors
MOGHIMI, H. FAZAELI; NOFERESTI, M.
- Abstract
Let R be a commutative ring with identity and R(RM ) denote the bounded lattice of radical submodules of an R-module M . We say that M is a radical distributive module, if R(RM ) is a distributive lattice. It is shown that the class of radical distributive modules contains the classes of multiplication modules and finitely generated distributive modules properly. Also, it is shown that if M is a radical distributive semisimple R-module and for any radical submodule N of M with direct sum complement Ñ, the complementary operation on R(RM ) is defined by N ′ := Ñ + rad{0}, then R(RM ) with this unary operation forms a Boolean algebra. In particular, if M is a multiplication module over a semisimple ring R, then R(RM ) is a Boolean algebra, which is also a homomorphic image of R(RR).
- Subjects
HOMOMORPHISMS; HYPERSURFACES; LORENTZIAN function; MATHEMATICAL models; MACHINE learning
- Publication
Journal of Mahani Mathematical Research Center, 2024, Vol 13, Issue 1, p347
- ISSN
2251-7952
- Publication type
Article
- DOI
10.22103/jmmr.2023.21494.1439