On Factorization Properties of Semi-Regular Congruence Monoids
نویسنده
چکیده
If given n ∈ N and Γ, a multiplicatively closed subset of Zn, then the set HΓ = {n ∈ Z : x ∈ N : x + nZ ∈ Γ} ∪ {1} is a multiplicative submonoid of N0 known as a congruence monoid. Much work has been done to characterize the factorial (every element has unique factorization) and half-factorial (lengths of irreducible factorizations of an element remain constant) properties of such objects. Our paper further examines the specific semi-regular case, when Γ contains both units and non-units. We delve into characterizing the half-factoriality problem for semi-regular congruence monoids, as well as finding sufficient conditions for a congruence monoid such that min∆ (HΓ) > 1.
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