# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.

* The ring of continuous functions from the real numbers to the real numbers is not Noetherian: Let I < sub > n </ sub > be the ideal of all continuous functions f such that f ( x ) = 0 for all x ≥ n. The sequence of ideals I < sub > 0 </ sub >, I < sub > 1 </ sub >, I < sub > 2 </ sub >, etc., is an ascending chain that does not terminate.

The ideal length for the connecting rope / chain is just enough to allow the user to lay it over his or her palm, with the sticks hanging comfortably and perpendicular to the ground.

The simplest possible polymer model is presented by the ideal chain, corresponding to a simple random walk.

The polymer can therefore be described by a simple random walk and ideal chain.

The chain behaves as if it were an ideal chain.

At a particular temperature called theta ( θ ) temperature, the solvent behaves as if an ideal chain.

The ideal chain model assumes that polymer segments can overlap with each other as if the chain were a phantom chain.

The radius of gyration is generally larger than that of the ideal chain.

Short ideal chain | random chain

This is the ideal chain mathematical model.

But there is reason to believe ( e. g., neutron diffraction studies ) that excluded volume effects may cancel out, so that, under certain conditions, chain dimensions in amorphous polymers have approximately the ideal, calculated size

Rondel daggers were ideal in battle for puncturing chain mail, and although they would not have been able to punch through plate armour, they could be forced between the joints in a suit of armour and helmets.

In commutative algebra, the height of a prime ideal ' in a ring ' is the number of strict inclusions in the longest chain of prime ideals contained in '.

The chain of hills of Altos presents ideal places to climb, the hill Caacupé, the Cristo Rey ( Ecological Reserve declared educational ) and the hill Cavajhu and Atyrá.

Although an 1 / 8-inch chain will work on a 3 / 32-inch chainring or sprocket, it is not ideal.

A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain.

While a single magnetosome chain would appear to be ideal for magneto-aerotaxis, a number of magnetotactic bacteria have magnetosomes or magnetosome arrangements that depart from the ideal.

* Entropic elasticity of an ideal chain

Walker in the mid-1960s expanded on traditional coal waterjet cutting to determine ideal nozzle shape for high-pressure waterjet cutting of stone, and Norman Franz in the late 1960s focused on waterjet cutting of soft materials by dissolving long chain polymers in the water to improve the cohesiveness of the jet stream.

For Plato, `` imitation '' is twice removed from reality, being a poor copy of physical appearance, which in itself is a poor copy of ideal essence.

In short, the fictional private eye is a specialized version of Adam Smith's ideal entrepreneur, the man whose private ambitions must always and everywhere promote the public welfare.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Again, Henley's attitude of defiance which colors his ideal of self-mastery is far from characteristic of a Stoic thinker like Marcus Aurelius, whose gentle acquiescence is almost Christian, comparable to the patience expressed in Milton's sonnet on his own blindness.

But the most fundamental objection he has to poets appears in the Tenth Book, and it is derived from his doctrine of ideal forms.

In Plato's mind there is an irresolvable conflict between the poet and the philosopher, because the poet imitates only particular objects and is incapable of rising to the first level of abstraction, much less the highest level of ideal forms.

True reality, of course, is the ideal, and the poet knows nothing of this ; ;

Even in such technical curricula as engineering, the senior is much more likely than the freshman to choose, as an ideal, liberal education over specific vocational preparation.

The old ideal of the independent entrepreneur is extant -- but so is the recognition that the main chance may be in a corporate bureaucracy.

On the other hand, the bright vision of the future has been directly stated in science fiction concerned with projecting ideal societies -- science fiction, of course, is related, if sometimes distantly, to that utopian literature optimistic about science, literature whose period of greatest vigor in the late nineteenth and early twentieth centuries produced Edward Bellamy's Looking Backward and H. G. Wells's A Modern Utopia.

But the only ideal he can think of is `` Sales ''!!

Many of these aspects will be seen as comparable to those of the ideal detective, but where the detective is active and militant, the jazz musician is passive, almost a victim of society.

Old Chris is my ideal.

The ideal girl -- possessed of talent, poise, intelligence, personality and beauty of face and figure -- is chosen each year to represent Rhode Island.

Minnesota, fabled land of waters, is in itself, ideal vacationland, having within its borders 10,000 lakes!!

The great absorbency of this tissue and the fact that it is easier to control than a sponge makes it an ideal tool for the watercolorist.

It is appropriate to call attention to certain thermodynamic properties of an ideal gas that are analogous to rubber-like deformation.

The internal energy of an ideal gas depends on temperature only and is independent of pressure or volume.

In other words, if an ideal gas is compressed and kept at constant temperature, the work done in compressing it is completely converted into heat and transferred to the surrounding heat sink.

According to this theory, living beings were classified on an ideal pyramid that represented the simplest animals on the lower levels, with complexity increasing progressively toward the top, occupied by human beings.

One of the simplest equations of state for this purpose is the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures.

This section explains only the simplest ideal cases.

A number of researchers have used a Gaussian smoothed step edge ( an error function ) as the simplest extension of the ideal step edge model for modeling the effects of edge blur in practical applications.

The simplest definition is that an ideal solution is a solution for which each component ( i ) obeys Raoult's law for all compositions.

The next simplest case is the case when the coefficient ring is a principal ideal domain.

Since 1945, Horrocks has been regarded by some as one of the most successful British generals of the war, " a man who really led, a general who talked to everyone, down to the simplest private soldier ", and the " beau ideal of a corps commander ".

In its simplest form it is a vertical radiator of half wavelength ( 180 electrical degrees ) to 5 / 9 wafelength ( 200 degrees ), although 195 degrees is considered ideal and 200 degree radiators have fallen into disuse except at the top of the band.

Similar examples could be created for any of the ' ideal ' circuit elements listed above, and many more, from RF frequency mixers to the simplest switch.