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math.AC2025
Valuation Ideal Factorization Domains
Gyu Whan Chang, Andreas Reinhart
An integral domain is a {\em valuation ideal factorization domain} (VIFD) if each nonzero principal ideal of can be written as a finite product of valuation ideals. Clearly…
math.AC2025
On the system of length sets of power monoids
Andreas Reinhart
The set of all finite subsets of containing the zero element is a monoid with set addition as operation. If a set $A\in\mat…
math.AC2025
Multiplicative lattices with absorbing factorization
Andreas Reinhart, Gulsen Ulucak
In [24], Yassine et al. introduced the notion of 1-absorbing prime ideals in commutative rings with nonzero identity. In this article, we examine the concept of 1-absorbing prime e…