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Abstract
Three related properties of a module are investigated in this article, namely the Nakayama property, the Maximal property, and the S-property. A module M has the Nakayama property if 𝔞M = M for an ideal 𝔞 implies that sM = 0 for some s ∈ 𝔞 + 1. A module M has the Maximal property if there is in M a maximal proper submodule, and finally, M is said to have the S-property if S −1 M = 0 for a multiplicatively closed set S implies that sM = 0 for some s ∈ S.
Notes
Communicated by S. Goto.