论文标题
在无扭转的单体的原子结构上
On the atomic structure of torsion-free monoids
论文作者
论文摘要
令$ m $成为一种取消和交换性（添加剂）单体。如果每个不可变形元素都可以写成不可约合的元素，则单件$ m $是原子质的，这也称为原子。同样，如果每个增加的主理想顺序（在包含在内）从一个点开始恒定，则$ m $满足主要理想的上升链条件（ACCP）。在本文的第一部分中，我们表征了无扭转的单体，它们满足ACCP为那些无扭转的单体，它们的下monoids都是原子。完全有序的阿贝尔群体的非负锥的亚monoi类通常称为阳性单体。每个积极的单体显然都是无扭转的。在本文的第二部分中，我们研究了某些阳性单体类别的原子结构。
Let $M$ be a cancellative and commutative (additive) monoid. The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements, which are also called atoms. Also, $M$ satisfies the ascending chain condition on principal ideals (ACCP) if every increasing sequence of principal ideals (under inclusion) becomes constant from one point on. In the first part of this paper, we characterize torsion-free monoids that satisfy the ACCP as those torsion-free monoids whose submonoids are all atomic. A submonoid of the nonnegative cone of a totally ordered abelian group is often called a positive monoid. Every positive monoid is clearly torsion-free. In the second part of this paper, we study the atomic structure of certain classes of positive monoids.
