|ISSN 1088-6826(online) ISSN 0002-9939(print)|
Minimal generating sets for free modules
Abstract: Let be a ring admitting a free module with generating set shorter than the length of a basis. If is the shortest basis among all such modules and the length of its shortest generating set then and every free module with basis of length has a generating set of length . If has module type then , that is an -module with basis of length not only has all bases of length but also has no generating set of length . The integer together with the module type define a new ring invariant which satisfies many of the properties of the module type.
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