Commutative algebra and algebraic geometry form a deeply interwoven field that investigates the structure of polynomial rings, their ideals, and the geometric objects defined by these algebraic sets.

Algebra is the discipline of pure mathematics that is concerned with the study of the abstract properties of a set, once this is endowed with one or more operations that respect certain rules (axioms) ...

Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. Mathematicians now present 'big algebras,' a two-way mathematical 'dictionary' ...

Certain theorems in algebra can be proved by showing that they hold in positive characteristic, and in characteristic p one has extra structure given by the Frobenius map x↦xp. There are several tools ...