Sentence examples for universal coefficient from inspiring English sources

Now, by the universal coefficient formula, the torsion subgroup of (H_n X, {mathbb {Z}})) equals the torsion subgroup of (H^{n+1} X, {mathbb {Z}})).

As a consequence, we show that every complex Kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real C∗-algebra.

We prove the gauge-invariant uniqueness theorem, and obtain conditions for our C∗-algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem.

Let A and B be two unital separable simple nuclear C∗-algebras with TR(A),TR(B ⩽1 which satisfy the universal coefficient theorem.

In this paper we analyze how this topology interacts with the terms of the Universal Coefficient Theorem (UCT) and the splittings of the UCT constructed by Rosenberg and the author, as well as its canonical three term decomposition which exists under bootstrap hypotheses.

We study the generalized Rørdam group KLKK A,B)="(A,B /0¯, and prove that if a separable exact residually finite dimensional C∗-algebra satisfies the universal coefficient theorem in KK-theory, then it embeds in the UHF algebra of type 2∞.

With six universal coefficients, the correlation is a function of temperature and a similarity variable, α, which is proportional to the number of atoms per unit mass.

The correlation may also be used for the development of high-accuracy fluid-specific correlations where warranted by customizing one or more of the universal coefficients.

Observe that (H^* X, {mathbb {Q}}) cong wedge ^* H^1 X, {mathbb {Q}}) Leftrightarrow H^* X, {mathbb {C}}) cong wedge ^* H^1 X, {mathbb {C}})) by virtue of the universal coefficients theorem.

end{aligned} Third Lefschetz' theorem or Hard Lefschetz' theorem: The first theorem and the universal coefficients theorem imply for the cohomology groups that ( H^i (X, {mathbb {Z}}) rightarrow H^i (W, {mathbb {Z}})) is bijective for ( i < n-1), while ( H^{n-1} (X, {mathbb {Z}}) rightarrow H^{n-1} (W, {mathbb {Z}})) is injective.

As a consequence of our result and of a theorem of Elliott and Gong, any such C∗-algebra, if it additionally satisfies the Universal Coefficients Theorem, is approximately homogeneous of topological dimension at most 3. Our result in particular confirms the Elliott conjecture for the class of simple unital Z-stable ASH algebras with real rank zero.