Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

Because of this time working closely and collaborating – a period that is normally far longer, and far more intimately involved, than the entire production and filming – most directors and editors form a unique artistic bond.

Because of the ballpark's age and constrained location in the dense Fenway – Kenmore neighborhood, the park has had many renovations and additions over the years not initially envisioned, resulting in unique, quirky features, including " The Triangle ," " Pesky's Pole ", and most notably the famous Green Monster in left field.

Because of the structure of the programmes and its unique global status, the University has an academic calendar that enables bringing on board the most highly acclaimed academicians and practitioners from around the world.

Because of this unique process, Madeira is a very robust wine that can be quite long lived even after being opened.

Because of its unique boreal forest habitat, the park has many breeding birds not found in most areas of New York and other mid-Atlantic states, such as boreal chickadees, gray jays, Bicknell's thrushes, spruce grouse, Philadelphia vireos, rusty blackbirds, American Three-toed Woodpeckers, black-backed woodpeckers, ruby-crowned kinglets, bay-breasted warblers, mourning warblers, common loons and the crossbills.

Because of its long isolation, the Seychelles hosts several unique species including the Coco de mer, a palm which has the largest seeds of any plant and the world's largest population of giant tortoises.

Because of its " smeared on " root, the word is also used for the unique practice by hedgehogs of coating their quills with a froth when encountering new smells or tastes in their environment.

Because of the large variety of sea life, including unique regional species, the park is popular with Scuba divers.

Because it is located at one of the major crossroads of communication in the Catalan Pyrenees, la Seu d ' Urgell has had a unique and historic role in the county of Urgell.

Because Radha has the unique position of being able to enchant even Krishna she is therefore known as Madan-Mohan-Mohini: the enchanter of the enchanter of Cupid.

Because of its unique origins as a military fort turned Indian boarding school turned state public school, Fort Lewis College also follows a 1911 mandate to provide a tuition-free education for qualified Native Americans.

Because of its unique location and small size, Ririe has become, in effect, a " bedroom " community with little retail commerce of its own.

Because of its unique history, the area is " one of the richest archeological sites in Southern Maryland.

Because of this Rhenen has a unique character with pretty much elevation through town.

Because of this word change the name La Russell appears to be unique in the United States.

Because of its unique name, and proximity to Pittsburgh, Mars has on occasion received national media attention.

Because of Addison's overwhelmingly commercial atmosphere, residents of Addison enjoy a unique lifestyle not common in other suburbs.

Because of the centuries of isolation, the islanders still speak in a unique island way that is similar to the speech spoken when Tangier was settled in 1686.

Because of Hong Kong's and Macau's long histories as colonies of the British and Portuguese empires, respectively, and the unique " one-country, two-systems " policy, the two city-states continue to enjoy a high degree of autonomy even after their return to China.

Because Haredi Judaism accords unique status to traditional Jewish thought, while downplaying the need to look to secular disciplines, it seeks theological answers from faithful reinterpretations of Judaism alone.

Because of this unique situation the economic historian Alfred Chandler called the German dye companies " the world's first truly managerial industrial enterprises ".

Because of the unique shooting technique of kyudo, protection on the left ( bow ) arm is not generally required.

Because it is a natural product, with its own unique variations, every piece has its own individual characteristics.

Because of Athlon's very large L1 cache and the exclusive design which turns the L2 cache into basically a " victim cache ", the need for high L2 performance and size was lessened.

Because of the structure's unusual design, it was originally presumed to be an early form.

Because these schools operated on very small budgets and attempted to serve as many needy children as possible, economic factors were prominent in their design.

Because of the compact size of the pistons and mechanical simplicity of design, these models are typically not as large or as expensive as the others types.

Because its main purpose was the presentation of live music, the hall needed a design focused not only on public access and exterior aesthetics, but also acoustics.

Because his task was to construct the wilful choices of his Punch editors, who probably took their cue from The Times and would have felt the suggestions of political tensions from Parliament as well, Tenniel ’ s work, as was its design, could be scathing in effect.

Because American bladesmiths use this design extensively it is a common misconception that the design originated in America.

Because its input can be described with a formal grammar, it can be used in parser design.

Because of this, many modern large caliber hunting revolvers tend to be based on the fixed cylinder design.

Because the car lacked a fuel pump, the fuel tank was placed high up in the engine compartment so that fuel could be fed to the carburetor by gravity ; a trade-off of this design is an increased fire risk in front-end accidents.

Because Volta believed that the electromotive force occurred at the contact between the two metals, Volta's piles had a different design than the modern design illustrated on this page.

Because of the poor reflectivity of the speculum mirrors of that day, Herschel eliminated the small diagonal mirror of a standard newtonian reflector from his design and tilted his primary mirror so he could view the formed image directly.

Because of inadequate design, roughly 25 – 40 % of the incoming fish get blocked by the dam each year.

Because lens design only allowed rather small aperture lenses, the image on the ground glass screen was faint and most photographers had a dark cloth to cover their heads to allow focussing and composition to be carried out more easily.

Because of the design of analog video signals, which represent luma and color information separately, a common first step in image compression in codec design is to represent and store the image in a YCbCr color space.

Because a conceptual schema represents the semantics of an organization, and not a database design, it may exist on various levels of abstraction.

Because of the popularity of Times Roman at the time, Monotype chose to design a variant of Times Roman suited to mathematical composition, and recut many additional characters needed for mathematics, including special symbols as well as Greek and Fraktur alphabets, to accompany the system instead of designing it around the typeface that was being used, for which characters were already available.

Because " Lisa's Wedding " ( season six, 1995 ) is set fifteen years in the future, Homer's design was altered to make him older in the episode.

Because workstations are designed for high-end tasks such as weather forecasting, video rendering, and game design, it's taken for granted that these systems must be running under full-load, non-stop for several hours or even days without issue.

) Because a toric lens must have the proper orientation to correct for a person's astigmatism, a toric contact lens must have additional design characteristics to prevent the lens from rotating out of the ideal alignment.

Because of the competing interests of cross-platform compatibility and advanced functionality, numerous alternative web application design strategies have emerged.