abelian group

In this example we have an abelian group, but that is not always the case.

However, the system using exclusive or is an abelian group.

A related but different notion is a free abelian group.

It has found many uses in abelian group theory and related areas.

His first paper was published at 19 on infinite abelian groups.

Every ring is an abelian group with respect to its addition operation.

Abelian groups are an important special type of group.

Let and make it an abelian group with the ordinary addition of functions.

This gave a finite abelian group, as was recognised at the time.

Under the first operator (+) it forms an abelian group.

The real line R is a locally compact abelian group.

It is possible to describe just intonation in terms of a free abelian group.

The 'rank' of a finite abelian group has a different definition.

Example: the theory of the integers viewed as an abelian group.

This gives the structure set the structure of an abelian group.

In fact, the modules over Z can be identified with the abelian groups.

The term rank has a different meaning in the context of elementary abelian groups.

Therefore, associated to any abelian group, is a ring.

The category of abelian groups is not cartesian closed, for the same reason.

If a group's operation is commutative, we call it an abelian group.

He worked especially in the theory of Abelian groups and ring theory.

However, the theory of abelian groups of higher rank is more involved.

In general, a finite abelian group G is considered.

The sets have actually the structure of abelian groups with disjoint union as addition.

Every elementary abelian group has a fairly simple finite presentation.