Category: Commutative algebra

However, most modern algebraic geometry texts starting with Alexander Grothendieck's foundational EGA use the convention in this article .< ref > A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud ( 1995 ), which uses " h < sub > A </ sub >" to mean the covariant hom-functor.

Category: Commutative algebra

* * Nicolas Bourbaki, Commutative algebra

Category: Commutative algebra

* Commutative algebra and Gröbner bases

Commutative diagrams play the role in category theory that equations play in algebra ( see Barr-Wells, Section 1. 7 ).

In fact, this is the definition of a Dedekind domain used in Bourbaki's " Commutative algebra ".

Category: Commutative algebra

< li > Commutative algebra ( Algèbre commutative ) </ li >

Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings.

* Bourbaki, Nicolas, Commutative algebra.

Commutative algebra.

* Ernst Kunz, " Introduction to Commutative algebra and algebraic geometry ", Birkhauser 1985, ISBN 0-8176-3065-1

* Matsumura, Hideyuki, Commutative algebra.

* Zariski, Oscar ; Samuel, Pierre, Commutative algebra.

Category: Commutative algebra

* Nicolas Bourbaki, Commutative algebra, Ch.

Category: Commutative algebra

Category: Commutative algebra

Commutative self-adjoint operator algebras can be regarded as the algebra of complex valued continuous functions on a locally compact space, or that of measurable functions on a standard measurable space.

Category: Commutative algebra

Category: Commutative algebra

Commutative rings in which prime ideals are maximal are known as zero-dimensional rings, where the dimension used is the Krull dimension.

* Commutative property, a property of a mathematical operation whose result is insensitive to the order of its arguments

In mathematics, Commutative Algebra is the area of abstract algebra dealing with commutative rings and commutative modules and algebras over commutative rings.

; Commutative rings and algebras: In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law.

Commutative algebra is the field of study of commutative rings and their ideals, modules and algebras.

CoCoA ( Computations in Commutative Algebra ) is a free computer algebra system to compute with numbers and polynomials.

* Commutative, local Frobenius algebras are precisely the zero-dimensional local Gorenstein rings containing their residue field and finite dimensional over it.

Commutative finite flat group schemes often occur in nature as subgroup schemes of abelian and semi-abelian varieties, and in positive or mixed characteristic, they can capture a lot of information about the ambient variety.

:( Commutative rings )< sup > op </ sup > ≅ ( affine schemes )

: Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields.

: Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields.

Commutative monoids are often written additively.

* Irving Kaplansky, Commutative rings ( revised ed.

* M. F. Atiyah ; I. G. Macdonald: Introduction to Commutative Algebra.

* David Eisenbud, Commutative Algebra With a View Toward Algebraic Geometry, New York: Springer-Verlag, 1999.

* Michael Atiyah & Ian G. Macdonald, Introduction to Commutative Algebra, Massachusetts: Addison-Wesley Publishing, 1969.

* David Eisenbud, Commutative Algebra With a View Toward Algebraic Geometry, New York: Springer-Verlag, 1999.

* Matsumura, Hideyuki, Commutative Ring Theory.

* Miles Reid, Undergraduate Commutative Algebra ( London Mathematical Society Student Texts ), Cambridge, UK: Cambridge University Press, 1996.

Commutative rings are much better understood than noncommutative ones.