Sentence examples for be a graded vector from inspiring English sources

Let P be a graded vector space and write (2.6) B (a, b ) P = B A 1 ⊗ ⋯ ⊗ B A r ⊗ P ⊗ B B 1 ⊗ ⋯ ⊗ B B s for the bar construction of P. When (a, b ) is fixed or understood from the context, we simply write B P. We make a note that B P is naturally an object of C h l f where the lattice is Z r + s and the filtration is induced by the length filtrations on the bar constructions.

Thus is a graded vector space, with being the -dimensional ech homology group with compact carriers of.

Thus H* X) = {H q (X)} is a graded vector space, H q (X) being the q-dimensional Čech homology group with compact carriers of X.

Thus (H X)={H_{q}(X)} ) (here X is a Hausdorff topological space) is a graded vector space, (H_{q}(X) ) being the q-dimensional C̆ech homology group with compact carriers of X.

A graded R-module M is said to be a graded multiplication module if for every graded submodule N of M, there exists a graded ideal I of h(R)such that N = IM.

Let R be a graded ring.

[7, Lemma 1.2], Let R be a graded ring and M be a graded R-module.

Let R be a graded ring and M be a graded multiplication module over R with this property that every graded submodule of M is graded semiprime.

Let R be a graded ring and M be a graded multiplication module over R. Let P be a graded maximal submodule of M.

[2, Theorem 5], Let R be a graded ring and M be a graded multiplication R-module.

Let N be a graded submodule of M.