Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 7 4 2026 10 01 Module version of tensorizing maps and tensor products on $C^*$-algebras 479 491 5934 10.22060/ajmc.2025.24545.1437 EN Ahmad Shirinkalam Department of Mathematics, CT.C, Islamic Azad University, Tehran, Iran Institute of Cognitive Computational Science, CT.C, Islamic Azad University, Tehran, Iran Journal Article 2025 08 11 For $C^*$-algebras $\mathfrak{A}, A$ and $ B $ where $ A $ and $ B $ are $\mathfrak{A}$-bimodules with compatible actions, we consider amalgamated $\mathfrak{A} $-module tensor product of $ A $ and $ B $ and study its relation with the C*-tensor product of $A$ and $B$ for the min and max norms. We introduce and study the notions of module tensorizing maps, module exactness, and module nuclear pairs of $ C^*$-algebras in this setting. We illustrate our results for the concrete examples of $C^*$-algebras on inverse semigroups. https://ajmc.aut.ac.ir/article_5934_7b852316cf9d2d41bec07321928afe96.pdf