Abstract

In the context of factorization in monoid rings with zero divisors, we study associate relations and the resulting notions of irreducibility and factorization length. Building upon these facts, we determine necessary and sufficient conditions for broad classes of monoid rings to satisfy the ascending chain condition on principal ideals or be a bounded factorization ring. Along the way, we completely characterize the monoid rings that are présimplifiable or domainlike, building upon the results of Ghanem/Wyn-Jones/Al-Ezeh and Anderson/Al-Mallah about group rings with these properties.

中文翻译：

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具有零除数的半圆环的缔合，不可约性和分解长度

摘要

在具有零因数的单曲面环中进行因式分解的情况下，我们研究了关联关系以及由此产生的不可约性和因式分解长度的概念。在这些事实的基础上，我们确定了宽泛集的类半齐环的必要条件和充分条件，以便满足主要理想上的升链条件或成为有界分解环。在此过程中，我们根据Ghanem / Wyn-Jones / Al-Ezeh和Anderson / Al-Mallah关于具有这些性质的环的结果，完全描述了可简化的或类似域的类半圆环。