* Every finite subextension of F / k is separable.

Every adjunction 〈 F, G, ε, η 〉 extends an equivalence of certain subcategories.

Every adjunction 〈 F, G, ε, η 〉 gives rise to an associated monad 〈 T, η, μ 〉 in the category D. The functor

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 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 statement in F #, including statements and loops, is a composable expression with a definite return type as well.

Every field has an algebraic closure, and it is unique up to an isomorphism that fixes F.

* Every 4-dimensional central simple algebra over a field F is isomorphic to a quaternion algebra ; in fact, it is either a two-by-two matrix algebra, or a division algebra.

Every functor F: D → E induces a functor F < sup > C </ sup >: D < sup > C </ sup > → E < sup > C </ sup > ( by composition with F ).

* Every reduced commutative k-algebra A is a separable algebra ; i. e., is reduced for every field extension F / k.

President John F. Kennedy said of Hayden, " Every Federal program which has contributed to the development of the West — irrigation, power, reclamation — bears his mark, and the great Federal highway program which binds this country, together, which permits this State to be competitive east and west, north and south, this in large measure is his creation.

* Every character value is a sum of n m < sup > th </ sup > roots of unity, where n is the degree ( that is, the dimension of the associated vector space ) of the representation with character χ and m is the order of g. In particular, when F is the field of complex numbers, every such character value is an algebraic integer.

Every President of the United States from William Howard Taft to John F. Kennedy threw a ceremonial first pitch at least once at Griffith.

* " Every Time You Say I Love You " ( 1981 ) F & SF, May

Every sitting U. S. President since 1960 ( Eisenhower, John F. Kennedy, Lyndon B. Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Reagan, George H. W. Bush, Bill Clinton and George W. Bush ) has addressed a convention or attended an event at Cobo Center.

" Two Cars in Every Garage and Three Eyes on Every Fish " was the first episode produced for the second season, but " Bart Gets an F " aired first because of Bart's popularity and the producers wanted to premiere with an episode involving him in hopes of stealing viewers from The Cosby Show.

* Young, F. Every Man his own Mechanic ( 1881 )

* The New Dictionary of Cultural Literacy, Third Edition: What Every American Needs to Know Edited by James Trefil, Joseph F. Kett, and E. D. Hirsch.

" Every time I turn around, there's a new trial of the century ," says defense attorney F. Lee Bailey.

Every year since 1952, it has sponsored the Alfred Korzybski Memorial Lecture, with presenters from a broad range of disciplines, from science to medicine to entertainment, including names like actor Steve Allen, psychologist Albert Ellis, scientist and visionary R. Buckminster Fuller, linguist Allen Walker Read, and philosopher F. S. C. Northrop.

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.

* 2011 – Every Mother Counts – " Present / Infant " ( Remix )

Every adult and wise woman without husband although reserves the right to accept concubinage for her employer / master without any coercion or force, but Islamic scholars have consensus that for sex relations options of Nikkah and Muta should be adopted instead of concubinage in this era.

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

Every adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in a lifetime.

Every S / 360 ( except for the Model 20, which was not a standard S / 360 ) had a byte-multiplexer channel and 1 or more selector channels.

Every simple R-module is isomorphic to a quotient R / m where m is a maximal right ideal of R. By the above paragraph, any quotient R / m is a simple module.

Every six months member countries exchange information on deliveries of conventional arms to non Wassenaar members that fall under eight broad weapons categories: battle tanks, armored combat vehicles ( ACVs ), large-caliber artillery, military aircraft / unmanned aerial vehicles, military and attack helicopters, warships, missiles or missile systems, and small arms and light weapons.

Every album, except 1969's The Chicago Transit Authority, 1978's Hot Streets and 1995's Night and Day: Big-Band, released by Chicago Transit Authority / Chicago has been the band name followed by a Roman numeral or numbered in some other manner.

Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.

Every Gundam has a unique name that befits the nature of the suit and / or its origins, such as the XXXG-01W Wing Gundam, XXXG-01D Gundam Deathscythe and the XXXG-01S Shenlong Gundam.

; Every Day / A Heart Full Of Love ( Reprise ): Valjean arrives in the middle of a love scene between Cosette and Marius and decides not to stand in the way of their happiness.

Every few minutes, trains travel between Monza and Milano via the Suburban Railway ( Line S9 ) and via local trains that connect Monza to Lecco, Como / Chiasso ( CH ) and Bergamo / Brescia.

Every individual is responsible for the situation surrounding him / her.

Every qualifying Voyager 2 image with resolution better than ~ 50 km / pixel shows Pan clearly.

On November 7, 2006 he also produced Lumines II for PSP, the sequel to the popular original ( this time supplementing the original score with a heavy integration of music videos ), and a shooter / puzzle hybrid game called Every Extend Extra ( a heavily-modified ' synesthesia ' update to an existing PC freeware title, Every Extend ," by indie developer " Omega "), which was released on August 7, 2006.

Every year since 1982, the W. C. Handy Music Festival is held in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and R & B.

Every year Clifton Park Soccer Club hosts an international tournament called the Rose and Kiernan / Clifton Park Soccer International Soccer Classic.

Every episode features a different topic, from a dance track to a love ballad, that requires the contestants to write and perform lyrics from a multiple of genres, for a cash prize of $ 100, 000, a publishing deal with songwriting collective The Writing Camp, and a recording deal with RCA / Jive label.

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

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 ).

* Every pair of congruence relations for an unknown integer x, of the form x ≡ k ( mod a ) and x ≡ l ( mod b ), has a solution, as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab.

# Moral law of karma: Every action ( by way of body, speech, and mind ) will have karmic results ( a. k. a. reaction ).

* k = 1 ( criticality ): Every fission causes an average of one more fission, leading to a fission ( and power ) level that is constant.

* Every linear combination of its components Y = a < sub > 1 </ sub > X < sub > 1 </ sub > + … + a < sub > k </ sub > X < sub > k </ sub > is normally distributed.

Every known Sierpinski number k has a small covering set, a finite set of primes with at least one dividing k · 2 < sup > n </ sup >+ 1 for each n > 0.

* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.

Every maximal outerplanar graph satisfies a stronger condition than Hamiltonicity: it is node pancyclic, meaning that for every vertex v and every k in the range from three to the number of vertices in the graph, there is a length-k cycle containing v. A cycle of this length may be found by repeatedly removing a triangle that is connected to the rest of the graph by a single edge, such that the removed vertex is not v, until the outer face of the remaining graph has length k.

Note: Every permutation over a set with k elements is a cyclic permutation of definition type 2 if and only if it is a cyclic permutation of definition type 1 with gcd ( k, offset )

Every vector a in three dimensions is a linear combination of the standard basis vectors i, j, and k.

* Every irreducible polynomial over k has distinct roots.

* Every polynomial over k is separable.

* Every finite extension of k is separable.

* Every algebraic extension of k is separable.

Every degree of freedom in the energy is quadratic and, thus, should contribute k < sub > B </ sub > T to the total average energy, and k < sub > B </ sub > to the heat capacity.

Every k-tree is uniquely ( k + 1 )- colorable.