User taliberius 4 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T00:00:32Z http://mathoverflow.net/feeds/user/29763 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/121633/what-is-an-ideal-supporting-algebra What is an ideal-supporting algebra? Taliberius 4 2013-02-12T19:03:25Z 2013-05-10T14:09:51Z <p>I'm sorry if this question is too elementary, but I asked it at <a href="http://math.stackexchange.com/questions/301039/what-is-an-ideal-supporting-algebra" rel="nofollow">MathStackExchange</a> and it received no responses.</p> <p>On the Wikipedia page for <a href="http://en.wikipedia.org/wiki/Congruence_relation" rel="nofollow">congruence relation</a> it mentions how for groups and rings, congruences can be identified with normal subgroups and ideals respectively, and that the most general algebraic structure for which this can be done are ideal-supporting algebras. But I haven't been able to discover what an ideal-supporting algebra is.</p> http://mathoverflow.net/questions/123739/is-there-a-conceptual-reason-why-topological-spaces-have-quotient-structures-whil Is there a conceptual reason why topological spaces have quotient structures while metric spaces don't? Taliberius 4 2013-03-06T11:28:22Z 2013-03-07T03:25:43Z <p>Of the mathematical objects that I am familiar with, it is normally the case that the product of 2 objects is an object of the same type and that an equivalence relation on an object induces a quotient object of the same type.</p> <p>I think I have some understanding as to why the product of 2 fields is not a field, because a field is not an algebra in the universal algebra sense. But I don't see a reason as to why an equivalence relation on a metric space fails to induce a quotient structure, apart from the fact that it just doesn't work.</p> http://mathoverflow.net/questions/115749/the-surreal-numbers-satisfy-all-the-field-axioms-except-that-its-elements-constit The Surreal numbers satisfy all the field axioms except that its elements constitute a proper class. Is it safe to call it a field? Taliberius 4 2012-12-07T21:49:08Z 2012-12-08T01:57:18Z <p>Do all the field theorems apply to surreal numbers? If fields were redefined so that their elements were allowed to come from an arbitrary class, would the theory look different to an algebraist?</p> http://mathoverflow.net/questions/121633/what-is-an-ideal-supporting-algebra/121734#121734 Comment by Taliberius 4 Taliberius 4 2013-02-13T22:04:12Z 2013-02-13T22:04:12Z I love your epithets. http://mathoverflow.net/questions/121634/what-is-an-ideal-supporting-algebra Comment by Taliberius 4 Taliberius 4 2013-02-12T20:07:12Z 2013-02-12T20:07:12Z I'm sorry about the duplicate. The website did something strange the first time I submitted, I thought that it didn't get through.