Spring 2010 Newsletter
Did You Know...?
...there is an integral domain which has composites with no factorization into primes?
Andrea Rothbart of Webster University introduced an example of one in the January 2010 issue of The College Mathematics Journal. Here we go…
Let Q’[x] be the set of polynomials over the rational numbers with integral constant terms. The units of Q’[x] are +1 and –1. The prime elements of Q’[x] include the prime integers, and the composite elements of Q’[x] are the composite integers.
Any polynomial of the form qxn, n, q nonzero is composite, but can’t be factored into a product of primes, since every nonzero integer, r, is a factor,