indecomposable

The indecomposable objects are the cyclic groups of prime power order.

In general, rings are first broken down into indecomposable rings.

Every simple module is indecomposable, but the converse is in general not true.

M is also clearly a uniform module and thus is directly indecomposable.

The pseudo-arc is an example of a hereditarily indecomposable continuum.

This implies that aR is directly indecomposable, so local idempotents are also primitive.

Otherwise, it is said to be indecomposable.

Here, uniqueness means direct decompositions into indecomposable subgroups have the exchange property.

As a topological space the dyadic solenoid is an indecomposable continuum.

A vector space is indecomposable if and only if its dimension is 1.

Every indecomposable algebraically compact module has a local endomorphism ring.

Solenoids are among the simplest examples of indecomposable homogeneous continua.

The indecomposable objects are the connected spaces.

A is indecomposable if it is not decomposable.

The multiplicatively indecomposable ordinals are those of the form for any ordinal α.

The indecomposable modules in wild blocks are extremely difficult to classify, even in principle.

That is: suppose is another expression of as a product of indecomposable subgroups.

Every simple module is indecomposable.

An indecomposable continuum is a continuum that cannot be represented as the union of two proper subcontinua.

As an immediate consequence, we see that the endomorphism ring of every finite-length indecomposable module is local.

The composition factors of the projective indecomposable modules may be calculated as follows:

In all other cases, there are infinitely many isomorphism types of indecomposable modules in the block.

He solved the problem of finding which abelian groups have a finite number of indecomposable modules.

It turns out that the quiver structure for a basic, indecomposable, Artinian serial ring is always a circle or a line.

Let A be an indecomposable generalized Cartan matrix.