Module Degenerations and Finite Field Extensions

Abstract

Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a field, $K$ a finite extension of $k$ and $\Lambda$ a $k$-algebra. Then any $K\otimes_k\Lambda$-module is also a $\Lambda$-module. We study how the isomorphism classes, degeneration and hom-order differ depending on which algebra we are working over.