Sentence examples for sum of modules from inspiring English sources

In addition, we know that the socle of Y / X ′ is generated by C, thus Y / X ′ embeds into a finite direct sum of modules in Q.

Total system costs are composed of the sum of module costs including mounting structures, inverters, batteries, cabling and power management devices.

Recall that a QTAG-module M is (ω+1 -projective if there exists submodule N⊂H1(M) such that M/N is a direct sum of uniserial modules and a QTAG module M is (ω+1 -projective if there exists submodule N⊂H1k (M) such that M/N is a direct sum of uniserial modules [5].

In sum, reactions of modules involved in increased versatility tend to be more closely downstream of nutrients, suggesting that they typically belong to pathways metabolizing such nutrients.

Because of the multimodular nature of the proteins, some of them contain more than one type of catalytic module, therefore the total sum of catalytic modules in the 63 enzymes is 80 in Table 1 (62 GH-, 13 CE- and/or 5 PL- containing enzymes).

Recall that a Q T A G -module M is ( ω + 1 ) -projective if there exists submodule N ⊂ H 1 ( M ) such that M / N is a direct sum of uniserial modules and a Q T A G module M is ( ω + k ) -projective if there exists a submodule N ⊂ H k ( M ) such that M / N is a direct sum of uniserial modules [4].

For infinite countable couniserial dimension one can show under some condition that the module can be represented as a direct sum of uniform modules.

An example is given to show that the direct sum of two modules each with couniserial dimension (even copies of a module) need not have couniserial dimension.

Theorem 4.5 shows that a Dedekind finite module with couniserial dimension is a finite direct sum of indecomposable modules.

Let N be a submodule of a QTAG-module M such that M/N is a direct sum of uniserial modules.

On the other hand, if C is regular, say belonging to the tube T, then also K belongs to T. Since X is an extension of a module in T by a preinjective module, it is the direct sum of a module in T and a preinjective module.