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math.AC2025
On GL-domains and the ascent of the IDF property
Victor Gonzalez, Ishan Panpaliya
Following the terminology introduced by Arnold and Sheldon back in 1975, we say that an integral domain is a GL-domain if the product of any two primitive polynomials over …
math.AC2025
On the ascent of almost and quasi-atomicity to monoid semidomains
Victor Gonzalez, Felix Gotti, Ishan Panpaliya
A commutative monoid is atomic if every non-invertible element factors into irreducibles (also called atoms), while an integral (semi)domain is atomic if its multiplicative monoid…
math.AC2024
On the atomicity of one-dimensional monoid algebras
Ishan Panpaliya
The ascending chain condition on principal ideals (ACCP) is almost always complementary to atomicity within integral domains: in fact, Cohn initially stated that these two conditio…