13 Facts About Commutative ring

An element of Commutative ring is called a unit if it possesses a multiplicative inverse.

Localization of a ring is a process in which some elements are rendered invertible, i e multiplicative inverses are added to the ring.

For example, all ideals in a commutative ring are automatically two-sided, which simplifies the situation considerably.

Ideals of a ring are the submodules of, i e, the modules contained in.

For various applications, understanding the ideals of a Commutative ring is of particular importance, but often one proceeds by studying modules in general.

Related searches

Any Commutative ring has two ideals, namely the zero ideal and, the whole Commutative ring.

The Commutative ring, where is an integer, is the Commutative ring of integers modulo.

Similarly as for other algebraic structures, a Commutative ring homomorphism is thus a map that is compatible with the structure of the algebraic objects in question.

The Commutative ring of germs of holomorphic functions on a Riemann surface is a discrete valuation Commutative ring.

Any regular local Commutative ring is a complete intersection Commutative ring, but not conversely.

Ring R is a set-theoretic complete intersection if the reduced ring associated to R, i e, the one obtained by dividing out all nilpotent elements, is a complete intersection.

Depth of a local ring R is the number of elements in some maximal regular sequence, i e, a sequence a1,.

Any Commutative ring that is isomorphic to its own completion, is called complete.