Maximal

In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal element in the poset of proper right ideals, and similarly, a maximal left ideal is defined to be a maximal element of the poset of proper left ideals.

It is possible for a ring to have a unique maximal ideal and yet lack unique maximal one sided ideals: for example, in the ring of 2 by 2 square matrices over a field, the zero ideal is a maximal ideal, but there are many maximal right ideals.

For each idempotent e of the semigroup there is a unique maximal subgroup containing e. Each maximal subgroup arises in this way, so there is a one-to-one correspondence between idempotents and maximal subgroups.

Define f(x) to be the highest power of the maximal ideal M containing x (equivalently, to the power of the generator of the maximal ideal that x is associated to).

Definition There are other equivalent ways of expressing the definition of maximal one-sided and maximal two-sided ideals.

Furthermore, a subset of a Boolean ring is a ring ideal (prime ring ideal, maximal ring ideal) if and only if it is an order ideal (prime order ideal, maximal order ideal) of the Boolean algebra.

However it is not a maximal order (in the sense of ring theory); there are exactly 7 maximal orders containing it.

It is also true that J(R) equals the intersection of all maximal left ideals within the ring.sfn These characterizations are internal to the ring, since one only needs to find the maximal right ideals of the ring.

Maximal atlas The atlas containing all possible charts consistent with a given atlas is called the maximal atlas: i.e., an equivalence class containing that given atlas (under the already defined equivalence relation given in the previous paragraph).

This partially ordered set does not even have any maximal elements, since any g divides for instance 2g, which is distinct from it, so g is not maximal.

Usage of microscopes offers superior visualization of the surgical site and tumor margin, and leads to fewer complications and maximal preservation of healthy tissue.

While the director wanted a darker tone initially, the decision to remove the Decepticon scene was made based on audience reactions, resulting in a more focused Maximal origin story.

Comparing the effects of variable and traditional resistance training on maximal strength and muscle power in healthy adults: A systematic review and meta-analysis.

On the contrary, I believe that maximal tolerance of free expression is crucial to American democracy, and I am deeply skeptical of both formal and informal censorship.

Tamaramiebi also appealed to the oil companies that had not complied with the HOSTCOM regulations to do so immediately to incorporate the Host Communities Development Trust Fund (HCDT) for maximal use.

Eniko appeared in a black string bikini that was minimal on the material and maximal on the figure-flaunting.

Its pricing nonsubjective have to be maximal market portion in order to get a far better long-term public presentation.

Nothing says Christmas like a classic red and white theme - red stripes, bright lights and a maximal feel.

Getting Muslims to abandon their faith, or compelling people to abstain from drug use, may just be the maximal objectives of these centers.

According to Gould "Cerion is the land snail of maximal diversity in form throughout the entire world.