Abstract
Let A and B be two rings, let J be an ideal of B and let f : A → B be a ring homomorphism. In this paper, we study when the amalgamation of A with B along J with respect to f is a \({\phi}\)-ring. Hence, we study two different chain conditions over this structure. Namely, the nonnil-Noetherian condition and the Noetherian spectrum condition.
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Tamekkante, M., Louartiti, K. & Chhiti, M. Chain conditions in amalgamated algebras along an ideal. Arab. J. Math. 2, 403–408 (2013). https://doi.org/10.1007/s40065-013-0075-0
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DOI: https://doi.org/10.1007/s40065-013-0075-0