Blocking these force generating modules is a very common way to disturb cell division, for instance, in cancer therapy (e.g. using taxol to stall MT growth).
Let M be a graded finitely generated module.
Let R be a graded ring and M be a graded finitely generated module over R. Let N and K be graded submodules of M.
Since N and K are graded coprime submodules in a graded finitely generated module M, we have R M = M = N + K = I M + J M = ( I + J ) M. Open image in new window.
For example, we show that if M is a graded finitely generated module, then two graded submodules N and K of M are graded coprime if and only if grad M (N) and grad M (K) are graded coprime.
Using the WGCNA unsupervised method, they generated modules of co-expressed genes by combining cases and controls instead of gene-wise differential expression analysis.
We found that all three main module definitions generate modules which are both more globally and more locally (according to extreme expression biclustering definition, see Supplementary Note 2) co-expressed compared with permuted modules (Supplementary Fig. 19).
Certain module definitions, strict coregulation in particular, and datasets, E. coli, and synthetic data generate modules that are better co-expressed within the expression data, which could explain why module detection methods generally also perform better on these datasets and module definitions (Fig. 2c,d).
Topics include groups, groups acting on sets, Sylow theorems; rings, factorization: Euclidean rings, principal ideal domains, the structure of finitely generated modules over a principal ideal domain, fields, and Galois theory.
