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Science Forum Index » Math - Symbolic Forum » I need help
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| Guest |
 Posted: Wed Jan 31, 2007 8:50 am |
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Hi I am a graduate student from China.since I plan to attend the Ph.D
entrance examination,I have to solve most of the excercises in the
book written by THomas W.Hungerford.but It's a great challege for me.I
look forward to your help. my problems are the following examples.
1 The set consisting of zero and all zero divisors in a commutative
ring with identity contains at least ome prime ideal.
2 An integral domain R is a unique facrorization domain if and only
if every nonzero prime ideal in R contains a nonzero principal ideal
that is prime.
3 Let G be abelian group containing elements a and b of orders m and
n respectively. Show that G contains an element whose order is the
least common multiple of m and n.
many thanks! |
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