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Page "Global field" ¶ 4
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Every and field
** Every field has an algebraic closure.
** Every field extension has a transcendence basis.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every field is, of course, one-dimensional over its center.
Every time an MTA receives an email message, it adds a < tt > Received </ tt > trace header field to the top of the header of the message, thereby building a sequential record of MTAs handling the message.
Every subfield of an ordered field is also an ordered field in the inherited order.
Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.
Every ordered field is a formally real field.
Every subfield of an ordered field is also an ordered field ( inheriting the induced ordering ).
Every ordered field can be embedded into the surreal numbers.
Every ordered field is a formally real field, i. e., 0 cannot be written as a sum of nonzero squares.
Every instruction consists of a 9-bit opcode, a 4-bit register code, and a 23-bit effective address field, which consists in turn of a 1-bit indirect bit, a 4-bit register code, and an 18-bit offset.
Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations.
Every planetary body ( including the Earth ) is surrounded by its own gravitational field, which exerts an attractive force on all objects.
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 local field is isomorphic ( as a topological field ) to one of the following:
Every year, the British Political Studies Association awards the Walter Bagehot Prize for the best dissertation in the field of government and public administration.
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 ).
Every quadratic form q in n variables over a field of characteristic not equal to 2 is equivalent to a diagonal form
Every kind of material has unique magnetic properties, even those that we do not think of as being “ magnetic .” Different materials below the ground can cause local disturbances in the Earth ’ s magnetic field that are detectable with sensitive magnetometers.

Every and either
Every two equivalence classes and are either equal or disjoint.
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
Every morpheme can be classified as either free or bound.
* Every formal address or message " to the nation " or to either or both Houses of the Oireachtas must have prior approval of the Government.
Every karma produces a result which must be experienced either in this or some future life.
Belkis Lora, a relative of a passenger on the crashed flight, said " Every Dominican in New York has either taken that flight or knows someone who has.
" Aside from merely disputing readings of his own work, however, in " Letter on ' Humanism ,'" Heidegger asserts that " Every humanism is either grounded in a metaphysics or is itself made to be the ground of one.
The following propositions all imply one another: " Every object is either black or not a raven ", " Every Raven is black ", and " Every non-black object is a non-raven.
Every resultant is either a sum or a difference of the co-operant forces ; their sum, when their directions are the same -- their difference, when their directions are contrary.
Every Duke thereafter has either died without heirs or succeeded to the Crown, and so has not been able to leave the Royal Family.
Every French noun has a grammatical gender, either masculine or feminine.
Every destination in the topology table can be marked either as " Passive ", which is the state when the routing has stabilized and the router knows the route to the destination, or " Active " when the topology has changed and the router is in the process of ( actively ) updating its route to that destination.
Every map that is injective, continuous and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed.
Every car uses either a 5. 0 L Ford " Boss 302 " SVO or a 5. 0 L Chevrolet small block race-engine ( depending on the make )-capable of producing between 460 and 485 kW ( 620 — 650 bhp ) of power, but generally quoted as a little over 450 kW ( 600 bhp ) in race trim.
Other sauces are either prepared from scratch, or are variations on a basic curry sauce :< ref ><" Every restaurant has a large pan of this sauce always at hand, with the recipe varying only slightly from Chef to Chef.
Every day is spent either in study of scriptures or meditation or teaching to lay people.
Concerning the role of clave in salsa music, Charley Gerard states: “ The clave feeling is in the music whether or not the claves are actually being played .” Every ostinato part which spans a cycle of four main beats, has a specific alignment with clave, and expresses the rhythmic qualities of clave either explicitly or implicitly.
Every stream from either side of the valley has its large terraces to correspond with those of the Passumpsic River.
Every even-numbered year either two or three members are elected by the people to serve a four-year term.
' Every year its either held in Baldwin or Franklin.
Every acre was owned by someone, either a private individual or by government in the form of the Crown.
The International Committee of the Red Cross 1958 Commentary on 1949 Geneva Convention IV Relative to the Protection of Civilian Persons in Time of War states: " Every person in enemy hands must have some status under international law: he is either a prisoner of war and, as such, covered by the Third Convention, a civilian covered by the Fourth Convention, or again, a member of the medical personnel of the armed forces who is covered by the First Convention.

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