User katie - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T16:40:05Z http://mathoverflow.net/feeds/user/26178 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107328/when-does-the-modulus-of-a-sum-of-an-integer-and-an-algebraic-integer-equal-an-in When does the modulus of a sum of an integer and an algebraic integer equal an integer? katie 2012-09-16T16:11:26Z 2012-12-12T01:38:01Z <p>Let say Z is a sum of n-roots of unity and thus an algebraic integer, and D is an rational integer. If |z+D| is an integer, what can we conclude regarding Z? can we say |Z| is integer? Another related question is, for which non-zero D, we can conclude |Z| is integer from the given that |Z+D| is an integer?</p> http://mathoverflow.net/questions/110611/power-sums-are-enough-for-rationality power sums are enough for rationality? katie 2012-10-25T03:04:57Z 2012-10-25T04:52:40Z <p>If I have k algebraic integers like a_1, ..., a_k such that the sum of their n-power are integer for n=1, ...m can we deduce that a_1, ..., a_k are integers? how large m should be? (how many power sum should be integers to deduce all a_i's are integers)</p> http://mathoverflow.net/questions/109968/when-does-a-polynomial-split-over-q When does a polynomial split over Q? katie 2012-10-18T02:42:32Z 2012-10-24T02:06:23Z <p>If P(x) is a polynomial in Q[X], is there any iff theorem that states all the roots of P(x) are rational based on the coefficients?! In another words, what could you impose on the coefficients to make sure a polynomial in Q[x] will split over Q.</p> http://mathoverflow.net/questions/109590/the-powers-of-non-empty-subset-of-a-group-that-generate-a-subgroup The powers of non-empty subset of a group that generate a subgroup katie 2012-10-14T09:19:02Z 2012-10-15T15:35:11Z <p>If G is a group and A and B to non-empty subsets of G, then by AB we mean the set consist of all product ab where a is in A and b is in B.(Standard definition) Similarly we can define X^m where X is a non-empty subset and m is a positive integer. So X^m for positive integer m, means the set of all products of length m taken from X.</p> <p><strong>If G is a group of size n, and X is a non-empty subset of G then prove that X^n is a subgroup of G.</strong></p> <p>this is quite easy to prove for abelian groups, so I mostly like to see a short nice proof for the general case.</p> http://mathoverflow.net/questions/109196/is-there-any-bound-on-the-absolute-number-of-algebraic-integer-in-terms-of-its-de is there any bound on the absolute number of algebraic integer in terms of its degree? katie 2012-10-09T01:37:22Z 2012-10-14T17:19:18Z <p>If Z is a sum of t distinct roots of unity and |Z| is a rational integer, can someone find a bound on |Z| in terms of k=deg(Q(Z):Q))?</p> <p>Clearly we need to have distinct roots of unity otherwise this won't work! </p> <p>Correction: Let assume that Z is not rational itself otherwise obviously it's wrong. Here I hope to extend the proof of Kronecker thm! I have "Z is a sum of t distinct roots of unity and |Z| is a rational integer" I conjecture that either Z is rational or a root of unity!</p> http://mathoverflow.net/questions/106269/which-algebraic-integers-in-a-cyclotomic-field-give-you-integer-absolute-value which algebraic integers in a cyclotomic field give you integer absolute value? katie 2012-09-03T19:44:54Z 2012-09-09T12:15:32Z <p>Does anyone know an answer to this question? Question: In an cyclotomic field which algebraic integers have integer absolute value?</p> <p>Revision 1: -1</p> <p>I like to add this to the above question, Let's take w to be a primitive n-th root of unity, for which set of exponents A of {0,1,...n-1} we have the absolute value of the sum_{i \in A} w^i is an integer. this might not be any help to make it solvable but at least avoid some repetitions</p> http://mathoverflow.net/questions/107328/when-does-the-modulus-of-a-sum-of-an-integer-and-an-algebraic-integer-equal-an-in/107335#107335 Comment by katie katie 2012-09-17T03:34:57Z 2012-09-17T03:34:57Z So, what is this telling us regarding Z and |Z|?!!