1. indecomposable - Noun
2. indecomposable - Adjective
Not decomposable; incapable or difficult of decomposition; not resolvable into its constituents or elements.
Source: Webster's dictionaryEvery injective module can be decomposed as direct sum of indecomposable injective modules. Source: Internet
In classical arithmetic any indecomposable number is a prime (and vice versa), but in more general domains a number may be indecomposable, such as 3 here, yet not prime in the earlier sense. Source: Internet
The representation ring's additive group is the free abelian group whose basis are the indecomposable modules and whose addition corresponds to the direct sum. Source: Internet
Expressing a module in terms of the basis is finding an indecomposable decomposition of the module. Source: Internet
Then each is an abelian category and we have an inclusion functor identifying the simple projective, simple injective and indecomposable projective-injective modules. Source: Internet
Then the trace of the indecomposable element v ⊗ f is defined to be f(v); the trace of a general element is defined by linearity. Source: Internet