International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 749-752
doi:10.1155/S0161171286000893
The GCD property and irreduciable quadratic polynomials
1D-80, Malvija Nagar, New Delhi 110017, India
2Deprtment of Mathematics, Florida State University, Tallahassee 32306-3027, FL, USA
3Department of Mathematics, Faculty of Science, Al-Faateh University, Tripoli, Libyan Arab Jamahiriya
Received 13 April 1984; Revised 3 July 1986
Copyright © 1986 Saroj Malik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.