Joseph Gibson

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2Ari Tenzer
2Arielle Fujiwara
1Rebecca Hunter
1William F Streck
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Let N represent the positive integers. Let n ∈ N and Γ ⊆ N. Set Γ n = {x ∈ N : ∃y ∈ Γ, x ≡ y (mod n)} ∪ {1}. If Γ n is closed under multiplication , it is known as a congruence monoid or CM. A classical result of James and Niven [15] is that for each n, exactly one CM admits unique factorization into products of irreducibles, namely Γ n = {x ∈ N : gcd(x, n)(More)
Let n ∈ N, Γ ⊆ N and define Γn = {x ∈ Zn | x ∈ Γ} the set of residues of elements of Γ modulo n. If Γn is multiplicatively closed we may define the following submonoid of the naturals: HΓ n = {x ∈ N | x = γ, γ ∈ Γn}∪{1} known as a congruence monoid (CM). Unlike the naturals, many CMs enjoy the property of non-unique factorization into irreducibles. This(More)
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