"If somehow money desappears from the surface of the Earth, so there
will be no more war."

Is this sentence true ?

(we mean by "war" fight between groups of people that can be fatal)

If money is used as a metaphor for economic power it is largely true.
Certainly, the major wars of the 20th Century fell within this
category.

I would have to disagree with the above comment. Money is a medium for
trade. It is a tangible good just like gold, hats, cars, Velveeta
cheese, and stocks. Money is only used as a tool to simplify trade
between 2 or more parties. If money is eliminated then our planet
would revert back to a true barter system, but trade would have to
continue.

If you want to eliminate war then you need to rid the Earth of reality
TV, foam fingers, and G Unit sneakers...they are the TRUE root of all
evil.

War on Terror ? 2001-present. 

Iraq War 2003 ? Iraq War - Iraqi Freedom (Gulf War II) - 2003-present. 

War on Terror Afghanistan 

Tamil War - Sri Lanka, present. 

Bosnian Conflict 

Persian Gulf War ? Desert Storm - Kuwait Liberation - Gulf War I. 

Falkland Islands War - 1982. 

Iran - Iraq War 1980-1988. 

Soviet - Afghan War - 1979-1989. 

Khmer Rouge 

Vietnam War 

Korean War ? 1950-present. Note. 

Arab-Israeli Wars ? 1948-present. 
Yom Kippur War - 1973. 

Six Day War - 1967. 

Chinese Civil War ? 1945-1949. 

Cold War ? 1945-1991. 

World War II ? 1939-1945 

Sino-Japanese War ? 1937-1945. 

Spanish Civil War ? 1936-1939. 

World War I (Great War) ? 1914-1918 

Russo-Japanese War ? 1904-1905. 

Spanish-American War ? 1898 

Franco-Prussian War ? 1870-1871. 

American Civil War ? 1861-1865. 

Crimean War ? 1853-1856. 

Mexican-American War ? 1846-1848. 

Texas War of Independence ? 1835-1836. 

War of 1812 ? 1812-1815. 

War of Independence (American Revolution) ? 1775-1783. 

Seven Years War ? 1756-1763. 
The French and Indian War 

Thirty Years War ? series of wars 1618-1648. 

Hundred Years War ? 1336-1452. 

Punic Wars ? Rome and Carthage, 264-146 B.C. 

Peleponessian War ? 431-404 B.C. 

http://vikingphoenix.com/military/war/wars.htm

I'm not expert on war, but it seems to me that if money were no object
that many of these wars would still have occured.
Proffessorman, I completely agree that money is simply a medium of
exchange, however I believe the spirit of this question is more about
the desire or jealousy of material wealth.  And the fact is that
people get mad over many things.  Money is perhaps the most common,
but by no means the only thing people fight over.

Perhaps Iraq wouldn't have invaded Kuwait if there was no oil there...
 Perhaps Osama and his thugs wouldn't have launched the terrorism war
if the US wasn't the symbol of economic power that it is...
But would America have wanted its independance from Brittain even if
high taxes weren't an issue?  Would France and Brittain have had
enough issues against eachother to fight over the centuries without
money being the cause?  Would the US have gone to war to gain a big
chunk of Mexico just for "manifest destiny"?  Would the holy wars have
happened if people weren't seeking treasure?

I would have to say that yes, definately yes, many of these wars would
have occured even if money was not an issue.  Bitterness, a desire for
freedom, religious disputes, desire for land...  these can all lead to
war atleast to some degree without the influence of money.