Sentence examples for m is contained from inspiring English sources

Then, every proper graded submodule of M is contained in a graded prime submodule.

(3) If M is an (mathcal{A} -equivalent set, then M is contA} -equivalenttain ℬ-equivalent set.  .

If M is an (mathcal{A} -equivalent set, then M is contA} -equivalenttain ℬ-equivalent set.

To finish the proof of Lemma 7.11 we first consider the particular case when m is contained in h.

Let T be a positive linear contraction on M such that τ○T⩽τ and such that the numerical range of T as an operator on L2(M) is contained in a Stoltz region with vertex 1.

Since the center of Z g R ( h ) is contained in h R and since m is contained in the center of its centralizer we have m ⊂ h R. Applying Lemma 7.10 then shows that m ⊂ h.

Arguing as above, we have that (H) is a (q^{prime } -group, (Hbigcap K=1) and (K) is contained in (M).

Hence every minimal subgroup of F ∗ ( M ∩ N ) is contained Z ( M ), and every cyclic subgroup of F ∗ ( M ∩ N ) of order 4 is weakly Φ-supplemented in M by Lemma 2.1.

Therefore, the set of zeros of ϕ ˆ n, m, ℓ 1 is contained in that of ϕ ˆ 2 n, m, ℓ 2 and this guarantees the stability of ϕ 1.

A hole h with the effective mass m h moves in the QD bulk, while an electron e with the effective mass m e (1) is contained in the dielectric matrix.

On the other hand, the image of ( p j u j ) j = 2 t : U → M ′ ′ is contained in ⨁ j = 2 t p j u j ( U ). Since u 1 = ∑ j = 2 t p j u j, this map ( p j u j ) j = 2 t is injective, thus U is a submodule of ⨁ j = 2 t p j u j ( U ).