5 articles
Associated graded ring
The associated graded ring, or associated graded algebra, is a graded ring built from a filtered ring's successive quotients, often turning a complicated ring into a polynomial ring.
Cohen structure theorem
The Cohen structure theorem is a 1946 result in commutative algebra describing every complete local ring as a quotient of a formal power series ring.
Henselian ring
A henselian ring, also called a Hensel local ring, is a local ring in which simple roots of polynomials over the residue field lift to roots in the ring.
I-adic completion
The I-adic completion of a ring R at an ideal I is the inverse limit of the quotients R/Iⁿ, replacing polynomials by formal power series and yielding the p-adic integers.
Witt vectors
Witt vectors are a construction turning a commutative ring R into a ring W(R) of sequences, built from universal integer polynomials; for finite fields they yield p-adic integers.