Sentence examples for be a commutative ring from inspiring English sources

Let A be a commutative ring with unity.

Let G be a group with identity e and R be a commutative ring.

Let A be a commutative ring and ({mathfrak {m}}) be a maximal ideal of A with non-zero annihilator.

Consider the action of (mathbf{G}) on ({mathfrak g}otimes _mathbb {K}{mathfrak g}) induced from the adjoint action of (mathbf{G}) on ({mathfrak g}.) Let R be a commutative ring extension of (mathbb {K}).

Also, a dominating set is a subset S of V(G) such that every vertex of (V(G {setminus} S) is adjacent to at least one vertex in S. The number of vertices in a smallest dominating set denoted by (gamma (G)), is called the domination number of G. Let A be a commutative ring with non-zero identity.

A cluster algebra is a commutative ring determined by an initial "seed," which consists of A-variables, X-variables, and some additional data.

If \ V\) is a commutative algebraic group over a field \ k\), [View the MathML] source is a commutative ring that acts on \ V\), and View the MathML source is a finitely generated free View the MathML source-module with a right action of the absolute Galois group of \ k\), then there is a commutative algebraic group [View the MathML source] over \ k\), which is a twist of a power of \ V\).

However it is a commutative ring even though we did not specify this.

When R is a commutative ring, the above theorem has the following consequence.

Moreover, if R is a commutative ring, then (|C_i|=2) for every (iin I).

If R is a commutative ring then there exists a ring homomorphism (f:Rrightarrow {{mathrm{End}}}_R(M)).