论文标题
长度工件和纯粹的不可还原性
Length-Factoriality and Pure Irreducibility
论文作者
论文摘要
如果对于每个不可变形的元素$ x \，则称为长度因素，如果在m $中，则在不可疑的$ x $中没有两个不同的因素化的$ x $具有相同的长度（即，不可减少因素的数量，计数重新估算）。 J. Coykendall和W. Smith在2011年以“另一半因素”术语引入了长度事实的概念：他们使用长度因素来提供独特的分解域的表征。在本文中，我们在更一般的接换性，取消性单体的情况下研究长度事实。此外，我们研究了与长度因素相关的分解属性，即PLS属性（Chapman等人最近引入）和半长度的属性。
An atomic monoid $M$ is called length-factorial if for every non-invertible element $x \in M$, no two distinct factorizations of $x$ into irreducibles have the same length (i.e., number of irreducible factors, counting repetitions). The notion of length-factoriality was introduced by J. Coykendall and W. Smith in 2011 under the term 'other-half-factoriality': they used length-factoriality to provide a characterization of unique factorization domains. In this paper, we study length-factoriality in the more general context of commutative, cancellative monoids. In addition, we study factorization properties related to length-factoriality, namely, the PLS property (recently introduced by Chapman et al.) and bi-length-factoriality in the context of semirings.
