PROPERTIES OF ALMOST ZIP BEZOUT - Rahmawati, As'adah
Bezout ring is one of classes of ring that has important role in ring theory and its application. A ring is a Bezout ring if every finitely generated ideal is principal. Commutative Bezout domain is said to be almost zip ring if any nonzero nonunit element of R is almost zip element. Nonzero and nonunit element a in ring R is said to be almost zip element if R=rad(aR) is a zip ring with rad(aR) is intersection of all prime ideals in ring aR. Zip ring is ring with annihilator of a ideal is zero, so annihilator of proper subset of ideal that is finitely generated ideal is zero. Almost zip Bezout domain was first introduced by Zabavsky and Romaniv in 2019. In this book, we give properties of Bezout domain, they are almost zip Bezout domain is J-Noetherian domain, elementary divisor domain, and fractionally regular domain.