two-sided ideal
1two-sided ideal — noun A subring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two sided ideal for emphasis …
2Two-sided — may refer to:* Two sided Laplace transform, integral transform closely related to the Fourier transform, Mellin transform, and ordinary Laplace transform * Two sided ideal, a type of ideal in ring theory * Two sided markets, economic networks… …
3Ideal (ring theory) — In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like even number or multiple of 3 . For instance, in… …
4Augmentation ideal — In mathematics, an augmentation ideal is an ideal in any group ring. If G is a group and R a commutative ring, there is a ring homomorphism varepsilon, called the augmentation map, from the group ring : R [G] to R , defined by taking a sum: sum r …
5Two-Face — This article is about the DC comics villain. For the Nigerian musician, see 2face Idibia. For the Brazilian soap opera, see Duas Caras. For craniofacial duplication, see Diprosopus. Superherobox| caption=Two Face, as depicted on the cover of… …
6Nil ideal — In mathematics, more specifically ring theory, an ideal of a ring is said to be a nil ideal if each of its elements is nilpotent.[1][2] The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring… …
7Principal ideal — In ring theory, a branch of abstract algebra, a principal ideal is an ideal I in a ring R that is generated by a single element a of R .More specifically: * a left principal ideal of R is a subset of R of the form R a := { r a : r in R }; * a… …
8Radical of an ideal — In ring theory, a branch of mathematics, the radical of an ideal is a kind of completion of the ideal. There are several special radicals associated with the entire ring such as the nilradical and the Jacobson radical , which isolate certain bad… …
9Primitive ideal — In mathematics, a left primitive ideal in ring theory is the annihilator of a simple left module. A right primitive ideal is defined similarly. Note that (despite the name) left and right primitive ideals are always two sided ideals.The quotient… …
10Quotient ring — In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two… …
