论文标题
在非交通界的分解域和原始环上
On noncommutative bounded factorization domains and prime rings
论文作者
论文摘要
如果每个取消的nonunit $ a \ in r $都可以写为原子的产物，并且此类因素化的长度上有一个绑定的$λ（a）$，则戒指具有有限的因素化。有界的分解特性是非唯一因素化研究中最基本的有限性能之一。每个可交换的Noetherian领域都有有限的因素化，但是这种结果是否在非交通设置中是否持开放态度。我们为非交通性的Noetherian Prime环提供了足够的条件，可以进行有限的因素化。此外，我们构建了一个（非共同的）有限呈现的半群代数，该代数是原子领域，但不满足原理右或左理想（ACCP）的上升链条件，因此它没有有限的因素化。
A ring has bounded factorizations if every cancellative nonunit $a \in R$ can be written as a product of atoms and there is a bound $λ(a)$ on the lengths of such factorizations. The bounded factorization property is one of the most basic finiteness properties in the study of non-unique factorizations. Every commutative noetherian domain has bounded factorizations, but it is open whether such a result holds in the noncommutative setting. We provide sufficient conditions for a noncommutative noetherian prime ring to have bounded factorizations. Moreover, we construct a (noncommutative) finitely presented semigroup algebra that is an atomic domain but does not satisfy the ascending chain condition on principal right or left ideals (ACCP), whence it does not have bounded factorizations.
