Page "Division ring" ¶ 3
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Some Related Sentences

Every and module
Every library module has at least two source files: a definitions file specifying the library's interface plus one or more program files specifying the implementation of the procedures in the interface.
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 simple module is indecomposable, but the converse is in general not true.
Every simple module is cyclic, that is it is generated by one element.
Every injective module can be decomposed as direct sum of indecomposable injective modules.
Every vector space is free, and the free vector space on a set is a special case of a free module on a set.
* Every module over a field or skew field is projective ( even free ).
* Every projective module is flat.
Every module possesses a projective resolution.
Every module of the form H * is algebraically compact.
Every indecomposable algebraically compact module has a local endomorphism ring.
* Every module M has an injective hull.
This is up to isomorphism the only indecomposable module over R. Every left R-module is a direct sum of ( finitely or infinitely many ) copies of this module K < sup > n </ sup >.
Every simple module is indecomposable.
Every finite-length module M has a composition series, and the length of every such composition series is equal to the length of M.
Every ring which is semisimple as a module over itself has zero Jacobson radical, but not every ring with zero Jacobson radical is semisimple as a module over itself.
* Every module can focus on what it is designed for.
Every superfield, i. e. a field that depends on all coordinates of the superspace ( or in other words, an element of a module of the algebra of functions over superspace ), may be expanded with respect to the new fermionic coordinates.

Every and over
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
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.
Every year many teams from all over Asia converge in Tokyo to compete.
Every division ring is therefore a division algebra over its center.
Every field is, of course, one-dimensional over its center.
* Every June, Ellensburg hosts Dachshunds on Parade, an event that draws Dachshund dog owners from all over the Northwest.
Every year sidecar racers travel from all over the UK to Knockhill in Scotland to race in the prestigious ' Jock Taylor Memorial Trophy ' race.
Every day, a blessing is recited over the Lulav and the Etrog.
Every major commercial transport and almost every military jet built in the United States over the last 40 years has been tested in this facility.
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.
* Every finitely-generated commutative algebra over a commutative Noetherian ring is Noetherian.
Every day all over the country, police officers are testifying.
Every character in the novel — both men and women — knows their place, and the traditional stereotypes of gender roles are repeated over and over again.
Every Turing machine computes a certain fixed partial computable function from the input strings over its alphabet.
* Every ninth year, people from all over Sweden assembled at the Temple at Uppsala.
Every year, millions of pilgrims from all over the world come to Częstochowa to see it.
Every Calan Mai, the two would fight over Creiddylad, until a battle on Judgement Day, in which the victor would keep her forever.
Controversy ensued over the use of the phrase " Every seat lost to the government is a seat sold to the Boers " as the Unionists waged a personalised campaign against Liberal critics of the war – some posters even portrayed Liberal MPs praising President Kruger and helping him to haul down the Union Jack.
Every year, the post office also creates a special Christmas hand-cancellation pictorial postmark for use during December, which also attracts mail from all over the world.
A quotation attributed to Kolmogorov is into English: " Every mathematician believes that he is ahead over all others.
Every August the Mountain Mama Road Bike Challenge brings cyclists from all over the country to challenge themselves on the steep roads of Highland County.
The argument over the quality of Fitzgerald ’ s translation of the Rubaiyat has, according to Dougan, diverted attention from a fuller understanding of the deeply esoteric message contained in Omar ’ s actual material – " Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".

Every and division
* 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 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 division is headed by a trustee, each responsible for publishing in the languages specific to that division.
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.

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