Encyclopedia > Commutative algebra

  Article Content

Commutative algebra

In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. It is foundational both for algebraic geometry and for algebraic number theory.

Related pages include:

The subject's real founder, in the days when it was called ideal theory, should be considered to be David Hilbert. He seems to have thought of it (around 1900) as an alternate approach that could replace the then-fashionable complex function theory. In line with his thinking, computational aspects were secondary to the structural. The additional module concept, present in some form in Kronecker's work, is technically an improvement on working always directly on the special case of ideals. Its adoption is attributed to Emmy Noether's influence.

Given the scheme concept, commutative algebra is reasonably thought of as either the local theory or the affine theory of algebraic geometry.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Smoking

... is (sort of) a disambiguation page; that is, one that just points to other pages that might otherwise have the same name. If you followed a link here, you might ...