Investigates the IMR property in ring extensions, suggesting implications for algebraic structures.
A commutative ring with identity is called an IMR-ring if it remains infinite modulo each of its maximal ideals. In this paper, we investigate the transfer of the IMR property to various ring extensions, including unital extensions, Nagata rings, Anderson rings, finite direct products, Nagata ideal transforms, trivial ring extensions, amalgamated duplications, amalgamated algebras, and pullbacks.
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Kim et al. (2026) studied this question.