For my bachelor thesis my goal is to understand the reasoning behind "Hilbert series" and how they connect to the idea of "dimension".
Concepts like modules and graded algebras are rather unfamiliar to me. I have not encountered these before.
I am familiar with:
Rings, groups and fields, both from linear algebra and a standard course in abstract algebra.
Gröbner basis, monomials ideals. From a course on computational algebraic geometry.
I am looking for some books/notes that could help me understand the concepts that surround Hilbert Series, preferably an introductory book along with a recommendation for further reading. It seems that I am requesting an "introductory commutative algebra" book.
If anybody also knows a good place for video lectures, this would be greatly appreciated.