Sentence examples for be a graded submodule from inspiring English sources

Let N be a graded submodule of M.

Then, for every positive integer n, the only graded prime submodule containing P n is P. Let P ́ Open image in new window be a graded prime submodule of M containing P n.

Let P be a graded prime submodule of M which contains both N2 and K2.

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 and M be a graded module over R; two graded submodules N and K of M are called graded coprime whenever N + K = M.

Then, N is graded prime if and only if K ∗ L ⊆ N implies that K ⊆ N or L ⊆ N for graded submodules K and Lof M. [7, Theorem 2.1], Let R be a graded ring and M be a graded multiplication R-module.

Let R be a graded ring and M be a graded multiplication module over R. Let N1and K1be two graded coprime submodules of M. Let N2and K2be two graded submodules of M such that every element of N1 resp. K1) has a power in N2(resp. K2).

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 module over R. Let N and K be graded submodules of M. then, (i) N ⊆ gra d M (N).

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.

Let R be a graded ring and M be a graded finitely generated cancelation module over R. Let N and K be graded submodules of M with graded presentation ideals I and J, respectively.