** Every field has an algebraic closure.

** Every field extension has a transcendence basis.

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 soldier in the army has, somewhere, relatives who are close to starvation.

Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every calculation has been made independently by two workers and checked by one of the editors.

Every retiring person has a different situation facing him.

Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

`` Every woman in the block has tried that ''.

: Every set has a choice function.

Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.

** Every surjective function has a right inverse.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

** Antichain principle: Every partially ordered set has a maximal antichain.

** Every vector space has a basis.

* Every small category has a skeleton.

* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).

** Every Tychonoff space has a Stone – Čech compactification.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.

Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.