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On the distributivity of the lattice of radical submodules
Let be a commutative ring with identity and denotes the bounded lattice of radical submodules of an -module . We say that is a radical distributive module, if 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. It is shown that if is a semisimple -module and for any radical submodule of with direct sum complement , the complementary operation on is defined by , then with this unary operation forms a Boolean algebra. In particular, if is a multiplication module over a semisimple ring , then is a Boolean algebra, which is also a homomorphic image of