Sentence examples for purely simple from inspiring English sources

The case of a purely simple spectrum is typical of 0>m∈C1(R).

The ion temperature achieved is also of an order of magnitude greater than that in lower field devices but this higher temperature is believed to be due to distortions in the RF waveform from the purely simple harmonic rather than just due to the higher RF field.

The ring R is called purely infinite simple in case R is simple, and each nonzero left ideal of R contains an infinite idempotent.

the graph monoid M E. V ( L K ( E ) ). V ( C ∗ ( E ) ). V M v N ( C ∗ ( E ) ). Algebraic: R is purely infinite simple in case R is simple and every nonzero right ideal of R contains an infinite idempotent.

Then L K ( E ) is purely infinite simple if and only if L K ( E ) is simple, and E contains at least one cycle.

By [8, Theorem 11], L C ( E ) is purely infinite simple if and only if L C ( E ) is simple, and E has the property that every vertex connects to a cycle.

Moreover, C ∗ ( E ) is purely infinite simple if and only if C ∗ ( E ) is simple, and E contains at least one cycle.

By [47, Proposition 5.3], C ∗ ( E ) is (topologically) purely infinite simple if and only if C ∗ ( E ) is simple, and E has the property that every vertex connects to a cycle.

In particular, we show that the above result obtained by Powers for the UHF algebras also holds for the class of purely infinite simple separable C∗-algebras classified by Kirchberg and Phillips and for the class of approximately homogeneous simple separable unital C∗-algebra with unique tracial state.

C ∗ ( E ) is (topologically) purely infinite simple.

C ∗ ( E ) is (algebraically) purely infinite simple.