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| ``Birkhoff''
by jocaps on 2009-03-27 22:34:14 |
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| I wonder, does Birkhoff specifically define l-rings? I never read Birkhoff so I thought I give it a look. Well.. I know some people could swear by this book (I know at least 2 people who have "enjoyed it"), but after taking one look at it.. I think my eyes hurt.. I don't know maybe the way he writes isn't suitable to me.
But anyway, back to my question. Could you maybe tell me the page where Birkhoff specifically defines l-rings? I know the definition of l-rings to be the same as yours except that its without the first condition for your po-rings. i.e. for me l-rings are. (I learned them from a paper from Melvin Henriksen and J.R. Isbell.)
rings with partial order (in the sense we know it) that makes them a lattice and such that the following condition holds:
x>=0, y>=0 => xy >= 0 (so the first condition is not there).
Maybe the first condition follows? Henriksen and Isbell refer a lot to the work of Birkhoff regarding works on l-rings .. so i do suppose they have the same notion of l-rings as Birkhoff. So I am not sure, either I am trying to see if the first condition of po-ring holds for l-rings or if your definition of l-ring is exactly what Birkhoff stated in his book "Lattice Theory". |
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