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a | c & b | c --> lcm(a,b) | c, right?
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DGoncz@aol.com
science forum Guru Wannabe


Joined: 25 Oct 2005
Posts: 122

PostPosted: Thu Jul 20, 2006 11:47 pm    Post subject: a | c & b | c --> lcm(a,b) | c, right? Reply with 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.

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

PostPosted: Fri Jul 21, 2006 12:29 am    Post subject: Re: a | c & b | c --> lcm(a,b) | c, right? Reply with quote

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

PostPosted: Fri Jul 21, 2006 7:14 am    Post subject: Re: a | c & b | c --> lcm(a,b) | c, right? Reply with quote

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.

Quote:

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

Doug
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