The Krull dimension is an ideal-theoretic invariant of an algebra. It has an important meaning in algebraic geometry: the Krull dimension of a commutative algebra is equal to the dimension of the corresponding affine variety/scheme. In my talk I'll explain how this idea can be transformed into a tool for measuring non-commutative rings. I'll illustrate this with important examples and techniques, and describe what is known for Iwasawa algebras of compact $p$-adic Lie groups.
- Junior Algebra and Representation Theory Seminar