Sentence examples for module with finite from inspiring English sources

Let M be an indecomposable automorphism-invariant module with finite Goldie dimension such that M is not quasi-injective.

This gives another example of an indecomposable module with finite Goldie dimension which is automorphism invariant but not quasi-injective.

In [1], several equivalent characterizations are given of when an automorphism-invariant module with finite Goldie dimension is quasi-injective.

Thus, we have an example of an indecomposable module with finite Goldie dimension which is automorphism invariant but not quasi-injective.

This means that the question of whether an automorphism-invariant module with finite Goldie dimension is quasi-injective reduces to study when an indecomposable automorphism-invariant module having finite Goldie dimension is quasi-injective.

The proposed procedures are implemented by combining Matlab based reliability modules with finite element models residing on the Abaqus software.

It is shown in Proposition 5.2 that a module (M) with finite length is semisimple if and only if for every submodule (N) of (M) the right (R -module (oplus _{i=1}^{infty }M/N) has couniseR -modulensioplus

R is a free module over L with finite rank, and.

In this paper, we say that a L-algebra R is a non-commutative ring only if. 1. R is a free module over L with finite rank, and   2.

Is there a theory for modules with both finite uniserial and couniserial dimensions that parallels to Krull Schmidt Remak Azumaya theorem?

(2) Is there a theory for modules with both finite uniserial and couniserial dimensions that parallels to Krull Schmidt Remak Azumaya theorem?  .