Sentence examples for with a direct sum of from inspiring English sources

In addition, we prove that ˆBrR(G) identifies with a direct sum of a Real cohomology group and the abelian group ˆExtR(G,S1) of Real graded S1-central extensions.

The square submatrix of B k is the same as that of a certain B k ( i | ), i = 1, …, r + 2 − k, which is a direct sum of two matrices [13] with the same type of D k or A k. Thus we only need to prove the case of A k.

We end this paper with the following remark: Now we may say that a QTAG-module M is a (ω+1 -projective Σ-module, if and only if it is a direct sum of countably generated modules with lengths at most ω+1 -projective

is also a direct sum of uniserial modules.

Hence, E is a direct sum of cyclic groups.

which is a direct sum of uniserial modules.

It is shown that every isometry is a direct sum of these types.

By Theorem 30.2 in [5], A is a direct sum of cyclic groups.

is a direct sum of uniserial modules implying that M/N is totally projective.

If N is h-distinctive, then M is also a direct sum of uniserial modules.

M/(N⊕H ω (M)) is a direct sum of uniserial modules and.