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added floating context menu “Algebra”
added table of contents
replaced “number” by “natural number”
hyperlinked author names and added publication data for:
This entry is dubious. Added a warning that the definitions don’t correspond to the definition in the reference. (I want to work first on the GCD domain entry which is the most classical definition for a commutative ring with gcd.)
In fact the definitions were correct until revision 10. But revision 11 deleted the requirement of asking the gcd only for pairs of regular elements.
Might be worth to revert the definitions back to revision 10 if no other sources for the current definition can be found.
Now, I think I understand why Anonymous changed the definition. It must be because it allows him to obtain, through the last equivalent definition of the four, that GCD rings form an algebraic theory. But with this simplified definition,I think you will lose all the properties which hold in gcd domains such as gcd domain lcm domain.
Ok I’m going to revert the definitions back to reivision 10 (up to the redundancy corrected before), with a single definition which is as in the reference.
changed higher algebra - contents to algebra - contents in context sidebar
Anonymouse
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