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 that supports the SMTP protocol for electronic mail is required by RFC 5321 and, as early as 1982, by RFC 822, to have the postmaster address.

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 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.

* Revised Code of Washington 9. 12. 010: " Every person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state.

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

Every person should be identified uniquely as resident in one place but where they happen to be on census day, their de facto residence, may not be the best place to count them.

According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".

Cobham was a common butt of veiled satire in Elizabethan popular literature ; he figures in Ben Jonson's Every Man in His Humour and may have been part of the reason The Isle of Dogs was suppressed.

Every convict detained in a TBS-clinic may get temporary leave, after serving a certain time or after some progress in treatment.

Every key frame is numbered with a multi-digit identifier that may be referred to later.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

The last two lines of the Act IV-scene 2 funeral song may also have inspired the lines W. H. Auden, the librettist for Stravinsky's The Rake's Progress, puts into the mouth of Anne Truelove at the end of the opera: " Every wearied body must late or soon return to dust ".

Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.

*: Articles 19 and 23 of the constitution provides, " Every person of I-Kiribati descent ... shall ... become or have and continue to have thereafter the right to become a citizen of Kiribati .... Every person of I-Kiribati descent who does not become a citizen of Kiribati on Independence Day ... shall, at any time thereafter, be entitled upon making application in such manner as may be prescribed to be registered as a citizen of Kiribati.

Every first Friday of the month, a trolley travels around Washington Street at different cafes and shops as artists showcase different pieces and may include auctions. This neighboorhod is scattered with urban blight ( within the residential section, from Caroll St east to the Brandywine Highway ).

Every point constructible using straightedge and compass may be constructed using compass alone.

Every non-inner automorphism yields a non-trivial element of Out ( G ), but different non-inner automorphisms may yield the same element of Out ( G ).

Every governing body is free to set its own standards, so the quality of races may differ.

Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

Every Dean of the Faculty ( equivalent to a Provost at most universities ) has always been an active-duty brigadier general, although technically, a civilian may hold the position.

The directive declared, " Every military commander has the responsibility to oppose discriminatory practices affecting his men and their dependents and to foster equal opportunity for them, not only in areas under his immediate control, but also in nearby communities where they may live or gather in off-duty hours.

From the Constitution of Lithuania, Article 32 ( 4 ): " Every Lithuanian person may settle in Lithuania.

Every kid is rated in running, batting, fielding, and pitching and has personality quirks that may affect the team.

Every late July ( ending on the last Saturday of July and beginning 10 days previous ) it hosts what may be the world's largest free-admission fair.

Every star of this type may usually be assigned a certain mean period.

Every 5 years the JNCC coordinates a compulsory review of schedules 5 and 8 to add new species that may need protection ( Legislation. gov. uk, 2010 ).