Monday, December 18, 2006
JSH: Deepening puzzle
It is NOT true that an algebraic integer cannot be the root of a non-monic polynomial with integer coefficients irreducible over Q.
Now I'm trying to figure out if the assertion that it is true is a sci.math only claim, or if it is a wrong belief that was held outside of Usenet before my research, which has since been adjusted as so far the strongest support of the sci.math'ers claim I've seen has been on the Wikipedia.
That changes a lot. An algebraic integer CAN be the root of a non-monic polynomial irreducible over Q.
So no, my results do not contradict with what follows from the ring of algebraic integers, as the argument is valid within that ring.
One argument claimed to be a proof of the false assertion that I saw years ago that convinced me is broken just by noting that an algebraic integer root of a non-monic polynomial irreducible over Q, can be the root of some monic polynomial with integer coefficients of higher degree.
So now I'm trying to figure out what exactly is the big deal with my original argument, and in retrospect it was the poster Rupert who first made the assertion that I now point out is false, and in considering that poster's recent replies, like how he has made some wackily wrong mathematical statements in recent posts attacking a simplified proof with my non polynomial factorization research, it occurs to me that he may have some serious issues, if you know what I mean.
Was this all some sick sci.math game?
Other replies I've seen from posters raise the possibility of simple jealousy and spite possibly with some kind of weird sense of superiority felt from managing to convince me of some wrong mathematical ideas.
Whatever the reasons they are probably going to be nasty, low and mean.
In any event, again, it is NOT true that an algebraic integer cannot be the root of a non-monic polynomial irreducible over Q, and I doubt you'd find a decent mathematician who would claim it is true, while I cite my amateur status and gullibility as reasons for how I was convinced.
Now I'm trying to figure out if the assertion that it is true is a sci.math only claim, or if it is a wrong belief that was held outside of Usenet before my research, which has since been adjusted as so far the strongest support of the sci.math'ers claim I've seen has been on the Wikipedia.
That changes a lot. An algebraic integer CAN be the root of a non-monic polynomial irreducible over Q.
So no, my results do not contradict with what follows from the ring of algebraic integers, as the argument is valid within that ring.
One argument claimed to be a proof of the false assertion that I saw years ago that convinced me is broken just by noting that an algebraic integer root of a non-monic polynomial irreducible over Q, can be the root of some monic polynomial with integer coefficients of higher degree.
So now I'm trying to figure out what exactly is the big deal with my original argument, and in retrospect it was the poster Rupert who first made the assertion that I now point out is false, and in considering that poster's recent replies, like how he has made some wackily wrong mathematical statements in recent posts attacking a simplified proof with my non polynomial factorization research, it occurs to me that he may have some serious issues, if you know what I mean.
Was this all some sick sci.math game?
Other replies I've seen from posters raise the possibility of simple jealousy and spite possibly with some kind of weird sense of superiority felt from managing to convince me of some wrong mathematical ideas.
Whatever the reasons they are probably going to be nasty, low and mean.
In any event, again, it is NOT true that an algebraic integer cannot be the root of a non-monic polynomial irreducible over Q, and I doubt you'd find a decent mathematician who would claim it is true, while I cite my amateur status and gullibility as reasons for how I was convinced.
# posted by James Harris @ 13:13 
