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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 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.

 Quote: Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada

Doug
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?

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
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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