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Fully inert submodules of torsion-free modules over the ring of p-adic integers

B. Goldsmith, L. Salce, P. Zanardo (2014)

Colloquium Mathematicae

Fully inert submodules of torsion-free J p -modules are investigated. It is proved that if the module considered is either free or complete, these submodules are exactly those which are commensurable with fully invariant submodules; examples are given of torsion-free J p -modules for which this property fails.

Gaussian and Prüfer conditions in bi-amalgamated algebras

Najib Mahdou, Moutu Abdou Salam Moutui (2020)

Czechoslovak Mathematical Journal

Let f : A → B and g : A → C be two ring homomorphisms and let J and J ' be ideals of B and C , respectively, such that f - 1 ( J ) = g - 1 ( J ' ) . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of A with ( B , C ) along ( J , J ' ) with respect to ( f , g ) (denoted by A ⋈ f , g ( J , J ' ) ) , introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.

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