Theorem of Bass

Theorem of Bass is a principle in algebra that concerns the relationship between complex structures called modules over a ring and their simpler, more fundamental components. It states that under certain conditions, if two modules become the same when extended to a larger, well-behaved context (like a bigger space), then they are already the same in their original setting. Essentially, it guarantees that "big-picture" equivalences can reflect and confirm the equivalences of the original, smaller parts, helping mathematicians understand how complex structures relate to their simpler building blocks.