Sentence examples for be a graded ring from inspiring English sources

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.

Let R be a graded ring.

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

[2, Theorem 5], 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 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 multiplication module over R. Let N and K be graded coprime submodules of M.

Let N be a graded submodule of M.

Let M be a graded finitely generated module.

Ideally, it should be a graded mixture of stones from 2 mm to 50 mm.

The direct sum :\pi_{\ast}^S=\bigoplus_{k\ge 0}\pi_k^S of the stable homotopy groups of spheres is a supercommutative graded ring, where multiplication is given by composition of representing maps, and any element of non-zero degree is nilpotent ; the nilpotence theorem on complex cobordism implies Nishida's theorem.

Let R be a G-graded ring and M be an R-module.