Algebra Seminar: Locally prime modules and locally reduced modules

Abstract: For a commutative unital ring R with a fixed ideal I, we introduce and study new classes of modules: I-prime modules and I-reduced modules and their dual notions;

I-coprime modules and I-coreduced modules respectively. We employ category-theoretic techniques to reveal novel structural properties of these modules. Our main results are generalizations of two fundamental theorems to this new setting: the Greenlees-May Duality

and the Matlis-Greenlees-May Equivalence. This enables us to establish, in the concrete module category, results that were previously only known in the derived category.

Lastly, we demonstrate that these new ``locally prime" (resp. "locally reduced" ) modules serve as a powerful tool for analyzing the structure of classical ``globally prime" (resp. "globally reduced") modules creating a bridge between local and global primality (resp. reducedness).

The primality part of the talk is joint work with Sholastica Luambano.

The seminar will be held via Zoom link (meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.