* Every real Banach algebra which is a division algebra is isomorphic to the reals, the complexes, or the quaternions.

Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.

Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.

Every division ring is therefore a division algebra over its center.

Every time one levels up a class division, one is given one extra attribute point until it reaches division level 50, such that a non reincarnated char has a total of 236 points, 216 points the character can invest as there is always 5 Tactics, Clout, Education and Mechanical Aptitude to start with.

We call a field E a splitting field for A if A ⊗ E is isomorphic to a matrix ring over E. Every finite dimensional CSA has a splitting field: indeed, in the case when A is a division algebra, then a maximal subfield of A is a splitting field.

* 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 GM division had an entry in this market by 1974, and the market was too large to ignore.

for the purpose of sale or of building development: Every division of a piece of land into two or more lots, parcels or parts is, of course, a subdivision.

Every year, conferences with topics pertaining to choral conductors are held-in even numbered years, a division conference is held in each division, and in odd numbered years, a national conference takes place in a major U. S. city.

Every other NFL team played a home-and-away series against the other members in its division, three interconference games, and the remainder of their 14 game schedule against other conference teams.

Every other NFL team played a home-and-away series against the other members in its division, three interconference games, and the remainder of their 14 game schedule against other conference teams.

Every major division, called a thema ( Greek: θέμα ), was further divided into tourmai while each tourma was divided into moirai or droungoi, which in turn were composed of several banda.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

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 taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

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.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

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

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

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

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

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every Easter Monday the doge headed a procession from San Marco to the convent of San Zaccaria where the abbess presented him a new camauro crafted by the nuns.

Every province has a Communist Party of China provincial committee, headed by a secretary beside the two special administrative regions.

Every chapter of the Genesis Rabba is headed by the first verse of the passage to be explained, and is introduced, with few exceptions, by one or more prefatory remarks starting from a verse taken from another Biblical passage as text — generally from the Writings or Ketuvim.

Every Easter Monday the doge headed a procession from San Marco to the convent of San Zaccaria where the abbess presented him a new linen camauro crafted by the nuns.

Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.

Every recorded request by Thomas for a delay in a flank movement or an advance was to gain time to take care of his horses.

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

Every night when he wanted a drink of water, didn't he practice being fearless by not turning on the bathroom light??

* In " Every Kind Word " by Lackthereof, Danny Seim's project parallel to Menomena, Seim sings "... and your hair is long like Absalom.

Every passage to the city was guarded by gates and towers, and a wall surrounded each of the city's rings.

Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

Every decision made by German or opposing forces required time to gather information, make a decision, disseminate orders to subordinates, and then implement this decision through action.

Every year there has been a major reduction in economic growth, it is followed by a reduction in the US trade deficit.

Every six months the presidency rotates between the states, in an order predefined by the Council's members, allowing each state to preside over the body.

* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".

* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.

* 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.

* Every regular language is context-free because it can be described by a context-free grammar.

" Nietzsche, who was heavily influenced by Schopenhauer, wrote: " Every concept originates through our equating what is unequal.

Every two years the meeting is held in a different member state, and is chaired by that nation's respective Prime Minister or President, who becomes the Commonwealth Chairperson-in-Office.

*" Lives of the Saints, For Every Day of the Year " edited by Rev.

George Every claims that the existence of " myths in the Bible would now be admitted by nearly everyone ", including " probably all Roman Catholics and a majority of Protestants ".

Most of his films have been at least partially financed by Telefilm Canada, and Cronenberg is a vocal supporter of government-backed film projects, saying " Every country needs system of government Grant ( money ) | grants in order to have a national cinema in the face of Hollywood ".

Every aspect of life was regulated to some degree by the party, and the will of its founding-president, Mobutu Sese Seko.

In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original.