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.

Transactions of the American Mathematical Society, Vol. 359, No. 2 (Feb., 2007), pp. 827-857 (31 pages) We discuss some of the basic ideas of Galois theory for commutative S-algebras originally ...

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) ...

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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' ...