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DGoncz@aol.com science forum Guru Wannabe
Joined: 25 Oct 2005
Posts: 122

Posted: Thu Jul 20, 2006 11:47 pm Post subject:
a  c & b  c > lcm(a,b)  c, right?



This is the only newsgroup I know of where you can ask a whole question
in the Subject: line and expect people to get it without reading the
Message.
I see it this way, with A = the multiset prime factoriztion of a, etc.
A is in C and
B is in C, so
max(A,B) is in C, right?
Sure!
I just wanted to be sure.
Doug 

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Robert B. Israel science forum Guru
Joined: 24 Mar 2005
Posts: 2151

Posted: Fri Jul 21, 2006 12:29 am Post subject:
Re: a  c & b  c > lcm(a,b)  c, right?



In article <1153439254.859331.213600@h48g2000cwc.googlegroups.com>,
The Dougster <DGoncz@aol.com> wrote:
Quote:  This is the only newsgroup I know of where you can ask a whole question
in the Subject: line and expect people to get it without reading the
Message.

.... but also to find it very annoying.
Quote:  I see it this way, with A = the multiset prime factoriztion of a, etc.
A is in C and
B is in C, so
max(A,B) is in C, right?

Right. Actually, the definition of lcm(a,b) in a commutative ring
is an element c such that every element divisible by a and by b is
divisible by c. They don't always exist, but they do exist in
unique factorization domains  and the proof of that is basically
what you're doing.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada 

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DGoncz@aol.com science forum Guru Wannabe
Joined: 25 Oct 2005
Posts: 122

Posted: Fri Jul 21, 2006 7:14 am Post subject:
Re: a  c & b  c > lcm(a,b)  c, right?



Robert Israel wrote:
Quote:  In article <1153439254.859331.213600@h48g2000cwc.googlegroups.com>,
The Dougster <DGoncz@aol.com> wrote:
This is the only newsgroup I know of where you can ask a whole question
in the Subject: line and expect people to get it without reading the
Message.
... but also to find it very annoying.

Oh. Then I will stop doing that. I didn't retitle this post, though.
Quote: 
I see it this way, with A = the multiset prime factoriztion of a, etc.
A is in C and
B is in C, so
max(A,B) is in C, right?
Right. Actually, the definition of lcm(a,b) in a commutative ring
is an element c such that every element divisible by a and by b is
divisible by c. They don't always exist, but they do exist in
unique factorization domains  and the proof of that is basically
what you're doing.
Really? I don't know from that kind of algebra. But I intend to learn. 
Thanks.
Doug 

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