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.
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