Abstract
Let A be a commutative ring and I an ideal of A. The amalgamated duplication of A along I, denoted by \({A \bowtie I}\) , is the special subring of \({A \times A}\) defined by \({A \bowtie I } := \pi \times_{\frac{A}{I}} \pi = \{(a, a + i) \mid a \in A, i \in I\}\) . We are interested in some basic and homological properties of a special kind of \({A \bowtie I}\) -modules, called the duplication of M along I with M is an A-module, and defined by \({M \bowtie I := \{(m, m') \in M \times M \mid m - m^{\prime} \in IM\}}\) . The new results generalize some results on amalgamated duplication of a ring along an ideal.
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Bouba, E.M., Mahdou, N. & Tamekkante, M. Duplication of a module along an ideal. Acta Math. Hungar. 154, 29–42 (2018). https://doi.org/10.1007/s10474-017-0775-6
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DOI: https://doi.org/10.1007/s10474-017-0775-6