Search Results for ""

Let G be a group with normal series (A_0, A_1, ..., A_r). A normal factor of G is a quotient group A_(k+1)/A_k for some index k<r. G is a solvable group iff all normal ...

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

A special ideal in a commutative ring R. The Jacobson radical is the intersection of the maximal ideals in R. It could be the zero ideal, as in the case of the integers.

Let R be a number ring of degree n with 2s imaginary embeddings. Then every ideal class of R contains an ideal J such that ||J||<=(n!)/(n^n)(4/pi)^ssqrt(|disc(R)|), where ...

A right or left ideal of a ring. The term is used especially in noncommutative rings to denote a right ideal that is not a left ideal, or conversely.

The commutator subgroup (also called a derived group) of a group G is the subgroup generated by the commutators of its elements, and is commonly denoted G^' or [G,G]. It is ...

Every module over a ring R contains a so-called "zero element" which fulfils the properties suggested by its name with respect to addition, 0+0=0, and with respect to ...

The number of elements of a group in a given conjugacy class.

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...