Sentence examples for ideal ring from inspiring English sources

We present a unified theory of Gröbner bases over a principal ideal ring with a view to applications in Coding Theory, for example to the structure of codes over a finite-chain ring, e.g. a Galois ring.

An examination of about 104 matching of {110} plane in FIM images of grain boundaries demonstrated that in most cases an ideal ring matching was accompanied by lack of the extra image points (i.e., an interstitial-like contrast) at the boundaries.

Our theory is effective and yields an extension of Buchberger's algorithm to principal ideal rings.

In [5], instead of one indeterminate, the authors have given the necessary and sufficient conditions for an ideal to have a single generator while, in [6], they have described all finite commutative principal ideal rings (frac {{mathbb {Z}}_{text {m}}[x_{1}, cdots, {x}_{n}]}{J}), where J is an ideal generated by univariate polynomials.

And the universal ideal rang out: "All human beings are born free and equal in dignity and rights".

Just as these ideals ring true for all members of major chef's organizations and the FoodShed Exchange, we will continue to share their voice and thank them for their drive to make the food world a better place.

Thermoplastic composite materials are now being considered as ideal wearing ring materials.

While Merck's vaccine is ideal for "ring vaccination", J&J's approach uses a two-part vaccine which could enable it to be longer lasting.

They pin photos of fantasy event spaces, dresses and flowers on Pinterest; they design their ideal engagement rings on sites like Ritani.com; they turn to MyKnot, Lover.ly and Project Wedding for ideas on invitations, gift registries and seating charts.

For example, the Axiom of Choice allows the taking of maximal ideals in rings and other structures; it entails the kinds of maximality principles that even the analysts were already using; it simplifies transfinite arithmetic; and despite its suspicious abstractness it turns out to be equivalent to 'concrete' and 'mathematical' statements such as the claim that every vector space has a basis.

In particular, she developed a completely new theory of ideals in rings, generalizing earlier work of Richard Dedekind.