Every principal ideal domain is a unique factorization domain ( UFD ).

# Every principal ideal domain is Noetherian.

# 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.

Every domain name appears in a zone served by one or more authoritative name servers.

Every domain name ends in a top-level or first-level domain label.

Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

Every function symbol has an associated arity, indicating the number of elements in the domain mapped onto each element of range.

Every polynomial in can be factorized into polynomials that are irreducible over F. This factorization is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field is a unique factorization domain whose units are the nonzero constant polynomials ).

The Highland MP and antiquarian, Charles Fraser-Mackintosh, comments on late eighteenth century evictions in the area of Kingussie, in his second series of " Antiquarian Notes " ( Inverness 1897, pp 369 et seq, public domain ) as follows: " Mr James MacPherson of Ossianic fame, who acquired Phoiness, Etterish, and Invernahaven, began this wretched business and did it so thoroughly that not much remained for his successors ....... Every place James MacPherson acquired was cleared, and he also had a craze for changing and obliterating the old names ......

Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.

* Every constant function whose domain and codomain are the same is idempotent.

* Every Jacobi-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

* Every Laguerre-like polynomial sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality is, and has Q =

* Every Hermite-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

Every domain D can be embedded in an ω-complete domain completion ( called the ω-completion or simply the completion of D ) that is, in a precise sense, the smallest ω-complete domain containing D. The isolated elements of completion are precisely the isolated elements of D, but in general completion contains limit points that are not found in D. completion is uniquely determined up to isomorphism.

Every village, town and city can build a Wizard Tower, and the Wizard only has to be inside one Wizard Tower, the other towers will also increase his domain.

Every domain may have a different timeline, adjusting events based on the domain's current time.

Every incoming email has an IP address that is difficult to forge, a bunch of domain names in the email headers, and a few more in the commands from the sender's SMTP server.

* Every concave function that is nonnegative on its domain is log-concave.

Every record has a unique identifier, which indicates the domain name of the original repository where the record was created.

Every aspect of his architecture, from overall concept to the smallest detail, supports his effort to express the modern age.

Every system is unique to the business drivers it supports, therefore the quality attributes of each system such as fault-tolerance, backward compatibility, extensibility, reliability, maintainability, availability, security, usability, and such other – ilities will vary with each implementation.

Every retaining wall supports a “ wedge ” of soil.

Every year, SINTEF supports research and development at 2, 000 or so Norwegian and overseas companies via its research and development activity.

Every seat in the concert hall has an unobstructed view, since there are no interior supports for the overarching dome.

Every URL consists of some of the following: the scheme name ( commonly called protocol ), followed by a colon, two slashes, then, depending on scheme, a server name ( exp.

Every postoffice had a separate Global Address List and these were synchronized using MSMail 3. X directory synchronization protocol and software called dispatch. exe.

Every member of Kobra was expected to have complete allegiance and devotion to the organization, and any protocol breach was punished with a gruesome death in a pit of vipers.

Every so often the diminishing sound of a car came under the trailer as it slowed down for the wreck then speeded up again as it got clear.

Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.

Every First Family seems to have one couple upon whom it relies for true friendship.

Every recorded request by Thomas for a delay in a flank movement or an advance was to gain time to take care of his horses.

Every few minutes she would awaken for a moment to review things: Stowey, yes, was on his way south, and the two boys were away in school, and nothing was burning on the stove, and Lucretia was coming for dinner and bringing three guests of hers.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every new scandal which would provide more `` copy '' for Marshall's pen would thus mean more publicity for Welch.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every single instance of altruistic behavior need not always increase inclusive fitness ; altruistic behaviors would have been selected for if such behaviors on average increased inclusive fitness in the ancestral environment.

Every time a speech sound is produced for a given phoneme, it will be slightly different from other utterances, even for the same speaker.

Every telephone company, whether large or small, determines its own ANAC for each individual central office, which tends to perpetuate the current situation of a mess of overlapping and / or spotty areas of coverage.

* Every institution must assign responsibility for caring for collections to members of its staff.

Every actor who has opened in the role of Pseudolus on Broadway ( Zero Mostel, Phil Silvers and Nathan Lane ) won a Best Actor Tony Award for their performance.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

Every week Holbrook writes the story line for the next three weeks for one of his strips and draws the next three weeks ' worth of strips for another.

Every cleric in Holy Orders and every member of a religious order must publicly join in or privately read aloud ( i. e. using the lips as well as the eyes — it takes about two hours in this way ) the whole of the Breviary services allotted for each day.

# Every net on X has a convergent subnet ( see the article on nets for a proof ).

Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).