• Journal of applied mathematics & informatics
• /
• 제26권3_4호
• /
• pp.779-784
• /
• 2008

We show that $\mathbb{Z}[\sqrt{-p}]$ is not a unique factorization domain (UFD) but a factorization domain (FD) with a condition $1\;+\;a^2p\;=\;qr$, where a and p are positive integers and q and r are positive primes in $\mathbb{Z}$ with q < p. Using this result, we also construct several specific non-unique factorization domains which are factorization domains. Furthermore, we prove that an integral domain $\mathbb{Z}[\sqrt{-p}]$ is not a UFD but a FD for some positive integer p.

• Korean Journal of Mathematics
• /
• 제32권1호
• /
• pp.97-107
• /
• 2024

Let A ⊆ B be an extension of integral domains with characteristic zero. Let H(A, B) and h(A, B) be rings of composite Hurwitz series and composite Hurwitz polynomials, respectively. We simply call H(A, B) and h(A, B) composite Hurwitz rings of A and B. In this paper, we study when H(A, B) and h(A, B) are unique factorization domains (resp., GCD-domains, finite factorization domains, bounded factorization domains).