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Quotient-transitivity and cyclic submodule-transitivity for p-adic modules

Volume 166 / 2021

Brendan Goldsmith, Ketao Gong Colloquium Mathematicum 166 (2021), 187-197 MSC: Primary 13C05; Secondary 20K30, 13C13. DOI: 10.4064/cm8348-1-2021 Published online: 11 March 2021

Abstract

Two new notions of transitivity, which we have named quotient-transitivity and transitivity with respect to cyclic submodules for $p$-adic modules, are introduced. Unlike the classical notions that derive from Abelian group theory, this approach is based on isomorphism of quotients and makes no use of height sequences. The two new notions lead to a sufficiently large class of interesting modules. Our principal result is that finitely generated $p$-adic modules are both quotient-transitive and transitive with respect to cyclic submodules.

Authors

  • Brendan GoldsmithSchool of Mathematical Sciences
    TU Dublin
    City Campus, Lower Grangegorman
    Dublin 7, Ireland
    e-mail
  • Ketao GongSchool of Mathematics and Statistics
    Hubei Engineering University
    No. 272, Jiaotong Road
    Xiaogan, Hubei, 432000, P.R. China
    e-mail

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