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.

By the above paragraph, we find that I is a maximal right ideal.

By the result of the previous paragraph, the limit function is also Lipschitz, with the same bound for the Lipschitz constant.

By the above paragraph, one can show that any constructible point can be obtained by such a sequence of extensions.

By 1908, this was described by the New York Times as a " long-established … preference " ( see article ) In modern usage in Scotland, " Scotch " is never used, other than as described in the following paragraph for certain articles ; it has gathered patronising and faintly offensive connotations (" frugal with one's money "), and a non-Scot who uses the word in conversation with Scots as a description of them may find this a good test of their courtesy.

By 20 May the Commons had agreed to one more minor alteration, but had not decided whether to accept the new paragraph.

By this time, to be precise, on July 15, 1937, because of Natascha ’ s status as “ Mischling ersten Grades ,” Emil had lost his post at the University — technically, compelled into early retirement — on the grounds of paragraph 6 of the Act to Restore the Professional Civil Service ( Gesetz zur Wiederherstellung des Berufsbeamtentums ) of April 7, 1933.

By the property noted in the above paragraph, if f is an irreducible ( non-zero ) polynomial with coefficients in the field F of prime characteristic p, and does not have distinct roots, it is possible to write f ( X )= g ( X < sup > p </ sup >).

By contrast, the anthrax entry has a large paragraph on the current reservoir.

With respect to ' the final paragraph, in which Jensen has Hanold asking Zoë to walk ahead of him and she complies with a smile, Freud put, " Erotic ... foot interest "'... By walking ahead of him in imitation of " Gradiva " on the plaque, she finds the key to his therapy '.

By the previous paragraph,, hence.

By taking Fourier transforms this follows from the fact that every polynomial has a distributional inverse, which is proved in the paragraph above.

By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument.

By moving the lowest 8 KB of RAM outside of reach of the ULA, the CPU could always access it at 2 MHz.

By the time of the war, they fielded the SdKfz 10 / 4 and 6 / 2, cargo halftracks mounting single 20 mm or 37 mm AA guns ( respectively ).

By 2003 in the US, an estimated 3. 21 million patients received antipsychotics, worth an estimated $ 2. 82 billion.

By 1995, many of the DOS-based BBSes had begun switching to modern multitasking operating systems, such as OS / 2, Windows 95, and Linux.

*" Why Pascal is Not My Favorite Programming Language " – By Brian Kernighan, AT & T Bell Labs, 2 April 1981

By managing all four populations as one-through strategic transfers, gene-loss is reduced from 8 % per decade to 2 % per decade, without any increase in bongo numbers in Kenya.

By contrast, the normal vaginal discharge will vary in consistency and amount throughout the menstrual cycle and is at its clearest at ovulation-about 2 weeks before the period starts.

By the end of World War 2, Canadians communicated by telephone, more than any other country.

By removing the bicarbonate more H < sup >+</ sup > is generated from carbonic acid ( H < sub > 2 </ sub > CO < sub > 3 </ sub >) which come from CO < sub > 2 </ sub >( g ) produced by cellular respiration.

By way of contrast, when introduced in 1985, the Amiga had compared favorably against 286-based systems with EGA graphics and rudimentary sound capabilities that frequently cost 2 – 3 times as much.

By comparison, when Mount St. Helens erupted in 1980, it released ~ 1. 2 km < sup > 3 </ sup > ( DRE ) of ejecta.

By 1990, Compaq Europe was a $ 2 billion business, and foreign sales contributed 54 percent of Compaq's revenues.

" By various stratagems the jealous king seeks his death, but the plots only endear David the more to the people, and especially to Saul's son Jonathan, who loves David ( 1 Samuel 18: 1, 2 Samuel 1: 25 – 26 ).

By 2 November, he had only reached Citivas Iovia ( Botivo, near Ptuj, Slovenia ).

By 1901 the population of Emsworth was about 2, 000.

By 1969 West German cinema attendance at 172. 2 million visits per year was less than a quarter of its 1956 post-war peak.

By inspection, each of the small natural numbers 1, 2, 3, 4, ... is the product of primes.

By use of a pulsed irrigation timer, existing overhead sprinklers may be used to deliver water at a low average precipitation rate ranging from 2. 5 to 5ml / Hour for frosts down to-5deg.

By 1970 the national census registered 8. 5 million people, about a 27 percent increase, while the most recent official census in 1984 recorded a figure of 12. 3 million — almost double the 1960 figure ( see table 2, Appendix ).

By the end of January 1959 the new army had reached a strength of around 2, 000 officers and soldiers.

By taking the intersection of p ( 1 ), p ( 2 ), p ( 3 ),... he formed p ( ω ), and then he noticed that p ( ω ) had a set of limit points p ( ω + 1 ), and so on.

By 2112, he was using two Ampeg SVTs, one which ran into 2 Sunn 215 cabs, and one which ran into 2 Ampeg V4b 215 cabs.

By their assistance and that of his own subjects, who entertained a great attachment for him, he recovered Epirus.

By 2012, despite natural gas prices at a ten-year low and a higher Canadian dollar, oil prices had recovered enough to restart economic growth.

By 1850, Parliament had enacted several statutes on a case-by-case basis to deal with issues regularly faced by certain types of organizations, like joint-stock companies, and with the impetus for most types of group litigation removed, it went into a steep decline in English jurisprudence from which it never recovered.

By the time of the Jupiter project cancellation in 1983, Foonly's proposal to build another F-1 was eclipsed by the Mars computer, and the company never quite recovered.

By 1671 Fox had recovered and Margaret had been released by order of the King.

By 1875 France had recovered from defeat in the Franco-Prussian War and a new government began to militarily expand and reassert itself again as a player in European politics.

By the Cisuralian, both oxygen and carbon dioxide had recovered to more normal levels.

By 1995, Paula Abdul had recovered from her battle with the eating disorder bulimia nervosa and prepared to return to the spotlight with her new album Head over Heels.

By the end of the 17th century, the Chinese economy had recovered from the devastation caused by the wars in which the Ming Dynasty were overthrown, and the resulting breakdown of order.

By means of the Axis invasion of the Soviet Union, Romania recovered Bessarabia and northern Bukovina from the Soviet Russia, under the leadership of general Ion Antonescu.

By the mid 1970s wildebeest and the Cape buffalo populations had recovered, and were increasingly cropping the grass, reducing the amount of fuel available for fires.

By the end of the year, however, Madrid was recovered by an army led by King Philip V and the Duke of Berwick ( the illegitimate son of James II of England, serving in the French army ).

By its end, the world had largely recovered from World War II and the Cold War developed from its modest beginning in the late 1940s to a hot competition between the United States and the Soviet Union by the beginning of the 1960s.

By this move, Frederick recovered his nominal domination over Italy.

By late April 1946, Ulam had recovered enough to attend a secret conference at Los Alamos to discuss thermonuclear weapons.

By the time she recovered, Mary had already left for her new life in the Netherlands.

By mid-December, Sherman was sufficiently recovered to return to service under Halleck in the Department of the Missouri.

By 257, Valerian had already recovered Antioch and returned the province of Syria to Roman control but in the following year, the Goths ravaged Asia Minor.

By that time there existed some half-dozen offshoots from the original Golden Dawn, and as a whole it never recovered.

By 1710, the city was fully recovered.

By 2005 the economy had recovered: there was considerable GNP growth, renewed foreign investment, and a significant drop in the unemployment rate.

By using photographs of the accident scene including the vehicle, " lost " evidence can be recovered and accurately determined.

By the next day, he had recovered sufficiently to resume the march.

By 1374, Charles had recovered all of France except Calais and Aquitaine, effectively nullifying the Treaty of Bretigny.

By the beginning of the 21st century, enough fragments had been recovered ( including the base ) that a partial reconstruction of Agoracritus ' Nemesis was performed in Rhamnus.