Sentence examples for modules of length from inspiring English sources

Let R ( i ) be the set of isomorphism classes of strongly regular modules of length i.

Now assume that (n > 1) and the result is true for all modules of length less than (n).

The regular Kronecker modules of length 2 different from R ∞ will be denoted by R λ with λ ∈ k.

In [5], it was shown that any ( ω + 1 ) -projective σ -module is a direct sum of countable modules of length atmost ( ω + 1 ).

We see that we obtain a parameterization of the set R ( 2 i ) of all strongly regular Kronecker modules of length 2i by the projective space P i.

The maximal submodules of Y are pairwise non-isomorphic and these are, up to isomorphism, all the strongly regular modules of length | Y | - 1.

The Γ ( C ) -module Hom ( C, Y ) is the indecomposable projective module of length 3.

Conversely, assume that X is a strongly regular module of length | X | = d.

When dealing with a local uniserial ring, the indecomposable module of length n will be denoted just be n.

Every summable module M is a Σ-module and every totally projective module of length ω+1 is a direct sum of countably generated modules.

There is the following converse: Let Q = ( D Λ ) b. Then any module of length at most b is present in Λ [ → Q 〉. Let M be a module of length at most b, thus the socle soc M of M is a semisimple module of length at most b and therefore a submodule of Q = ( D Λ ) b. It follows that M itself can be embedded into Q.