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* Every left ideal I in R is finitely generated, i. e. there exist elements a < sub > 1 </ sub >, ..., a < sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.
Some Related Sentences
Every and left
Every January 19, in the early hours of the morning, the person made a toast of cognac to Poe's original grave marker and left three roses.
If the book itself, Animal Farm, had left any doubt of the matter, Orwell dispelled it in his essay Why I Write: ' Every line of serious work that I ’ ve written since 1936 has been written directly or indirectly against Totalitarianism ... dot, dot, dot, dot.
Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.
* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.
Every one of the features encompassed by the theory still requires a reason for it to be maintained after hominids left the aquatic environment.
Every year since 1880, the organizations of the French left have held a demonstration in this symbolic place during the last week of May.
" Every part of his body has been replaced, with the exception of " all the diodes down left side ," which have been giving him severe pain for the whole of his existence.
Every actor provided multiple voices, although the distinctive baritone of Earle Hyman ( Panthro ) left the actor providing only very occasional guest voices in comparison with his fellow performers.
Every factual error left in the published records is officially considered to be a failure by the responsible officer.
Every week, he left her food near the statue, which was placed outside the house, but nobody knew he was doing it.
Every seat in the ballpark is green, except for two-one in left field which marks the spot of Cal Ripken's 278th career homerun, breaking Ernie Banks'all time record among shortstops, and one in right field, which marks the spot of Eddie Murray's 500th career homerun.
Every chain either has the middle tile on the outside ( O ) or the inside ( I ) of the chain ; if it is arranged so that the indicator tile is to the right of the middle tile, then the position of the ring segment on the indicator tile can either be the upper left ( UL ), upper right ( UR ), lower left ( LL ) or lower right ( LR ) corner.
Every day, she saw trucks loaded with Jews heading to the railway station from where the trains left for concentration camps.
Every member of the Queen's Royal Hussars of the United Kingdom light cavalry wears the Maid of Warsaw, the crest of the City of Warsaw, on the left sleeve of his No. 2 ( Service ) Dress.
Every Samhain, the phantom Aillén mac Midgna, or Aillén the Burner, would terrorize Tara, playing music on his harp that left every warrior helpless.
Every and ideal
* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.
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 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 field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.
In Leedskalnin's own publication A Book in Every Home he implies his " Sweet Sixteen " was more an ideal than a reality.
Every meal can be eaten without any cooking ; when circumstances permit, the ideal method of preparation is to cook the entrees in a pressure cooker, heated on the standard issue Coleman stove, or by simply boiling the rations in its package in water.
Every free spirit looked upon her as protectoress and ideal .... Marguerite was the embodiment of charity.