论文标题
偶然降低的单体半分的算术
Arithmetic of additively reduced monoid semidomains
论文作者
论文摘要
如果Pairs $（S，+）$和$（S，\ CDOT）$是具有身份的半群，则一个积分域$ r $的子集$ s $称为半域；此外，我们说，只要$ s $不包含添加剂倒置，$ s $就会加上减少。鉴于添加性降低的半分域$ s $和无扭转的单型$ m $，我们用$ s [m] $表示由多项式表达式组成的$ s $ s $ s $ s $ s $和指数的半域;我们将这些对象称为添加性降低的单体半分。我们研究了添加性降低单体半分的分解特性。具体而言，我们确定了添加性降低的单体半构域的必要条件，为有界分解半构域，有限分解半构域和独特的分解半构域。我们还提供具有全元弹性和无穷弹性的大型半构分。在整篇文章中，我们提供了旨在阐明添加性降低半分的算术的示例。
A subset $S$ of an integral domain $R$ is called a semidomain if the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities; additionally, we say that $S$ is additively reduced provided that $S$ contains no additive inverses. Given an additively reduced semidomain $S$ and a torsion-free monoid $M$, we denote by $S[M]$ the semidomain consisting of polynomial expressions with coefficients in $S$ and exponents in $M$; we refer to these objects as additively reduced monoid semidomains. We study the factorization properties of additively reduced monoid semidomains. Specifically, we determine necessary and sufficient conditions for an additively reduced monoid semidomain to be a bounded factorization semidomain, a finite factorization semidomain, and a unique factorization semidomain. We also provide large classes of semidomains with full and infinity elasticity. Throughout the paper we provide examples aiming to shed some light upon the arithmetic of additively reduced semidomains.
