Tendler's Theorem

Tendler's Theorem addresses the behavior of algebraic structures called modules over rings. It states that under certain conditions, a module's properties can be deduced from its behavior when localized at prime ideals—meaning examining the module only at specific "points" within its structure. Essentially, it ensures that if a module looks "nice" at all these points, then it is "nice" everywhere. This theorem helps mathematicians understand complex structures by analyzing their simpler, localized pieces, facilitating a deeper grasp of their overall nature through their local behaviors.