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I'm a bit uncertain about the definition for group isomorphism. The article says "a bijective group homomorphism". I think this nullifies statements (and their proofs) such as "a group homomorphism is an isomorphism iff it is bijective", and therefore should be changed to something that requires the existence of a sibling homomorphism from the codomain group to the domain one. Unfortunately, i've forgotten the details, but at least that's what i remember from my Algebra 101 class of 9 years ago. -- Jokes Free4Me ( talk) 12:28, 30 July 2009 (UTC)
I've heard people distinguish between an "isomorphism into" another group and an "isomorphism onto" another group. With the former, the "other group" is not isomorphic to the domain, but of course it has a subgroup that is. Michael Hardy ( talk) 16:44, 30 July 2009 (UTC)
Eisenstein's criterion mentions that "Then f(x) is irreducible over F[x], where F is the field of fractions of D. When f(x) is primitive [...], it is also irreducible over D[x]." I believe Irred(F[x]) implies Irred(D[x]), since if something is reducible over D[x] it must clearly be immediately reducible over F[x], using the same decomposition. -- Jokes Free4Me ( talk) 13:40, 30 July 2009 (UTC)
Mathematics desk | ||
---|---|---|
< July 29 | << Jun | July | Aug >> | July 31 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I'm a bit uncertain about the definition for group isomorphism. The article says "a bijective group homomorphism". I think this nullifies statements (and their proofs) such as "a group homomorphism is an isomorphism iff it is bijective", and therefore should be changed to something that requires the existence of a sibling homomorphism from the codomain group to the domain one. Unfortunately, i've forgotten the details, but at least that's what i remember from my Algebra 101 class of 9 years ago. -- Jokes Free4Me ( talk) 12:28, 30 July 2009 (UTC)
I've heard people distinguish between an "isomorphism into" another group and an "isomorphism onto" another group. With the former, the "other group" is not isomorphic to the domain, but of course it has a subgroup that is. Michael Hardy ( talk) 16:44, 30 July 2009 (UTC)
Eisenstein's criterion mentions that "Then f(x) is irreducible over F[x], where F is the field of fractions of D. When f(x) is primitive [...], it is also irreducible over D[x]." I believe Irred(F[x]) implies Irred(D[x]), since if something is reducible over D[x] it must clearly be immediately reducible over F[x], using the same decomposition. -- Jokes Free4Me ( talk) 13:40, 30 July 2009 (UTC)