Sentence examples for be a graded finitely from inspiring English sources

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.

Let M be a graded finitely generated module.

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.

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. Let P be a graded maximal submodule of M.

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.

[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.