Sentence examples for module over a from inspiring English sources

We apply the above results to produce an example of a contractive module over A(B2), which is not completely contractive.

A Hilbert module over a planar algebra P is essentially a Hilbert module over a canonically defined algebra spanned by the annular tangles in P. It follows that any planar algebra Q containing P is a module over P, and in particular, any subfactor planar algebra is a module over the Temperley Lieb planar algebra with the same modulus.

The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module.

Assume that M is a module over a ring (R = oplus _k R_k ).

By Lemma 5.6 every module over a factor ring of (R) also has couniserial dimension.

Our next step will be to show that any automorphism invariant module over a commutative noetherian ring R is quasi-injective.

Assume also that X is a Banach left module over A. We say that ( ( X k, ∥ ⋅ ∥ k ) : k ∈ N ) is a multi-Banach left module over ( ( A k, ∥ ⋅ ∥ k ) : k ∈ N ) if there is an M ≥ 0 such that ∥ ( a 1 x 1, …, a k x k ) ∥ k ≤ M ∥ ( a 1, …, a k ) ∥ k ⋅ ∥ ( x 1, …, x k ) ∥ k. for all k ∈ N, a 1, …, a k ∈ A, x 1, …, x k ∈ X.

Tor as a module over an exterior algebra, (with D. Eisenbud and F.-O. Schreyer), Journal of the EMS, to appear.

This is modeled on the de Rham resolution of a connection on a module over an algebra.

For instance, the connection agent is responsible for interacting with the sensor module over an internal API and periodically polling it to retrieve measurements from the M2M device.

In particular, this is the case when M is a module over an F-algebra, where F is a field with more than two elements; thus extending the previously mentioned result of Dickson and Fuller for indecomposable modules [5].