Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772859 | Journal of Pure and Applied Algebra | 2017 | 6 Pages |
Abstract
In this paper, we show that it is possible for a commutative ring with identity to be non-atomic (that is, there exist nonzero nonunits that cannot be factored into irreducibles) and yet have a strongly atomic polynomial extension. In particular, we produce a commutative ring with identity, R, that is antimatter (that is, R has no irreducibles whatsoever) such that R[t] is strongly atomic. What is more, given any nonzero nonunit f(t)âR[t] then there is a factorization of f(t) into irreducibles of length no more than deg(f(t))+2.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jim Coykendall, Stacy Trentham,