International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 749-752
doi:10.1155/S0161171286000893
The GCD property and irreducible quadratic polynomials
Saroj Malik1
, Joe L. Mott2
and Muhammad Zafrullah3
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
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.