Carptopus

Periodic Two-Letter Ringsets in the Lipschitz Quaternions: The General Odd-Period Classification

Let L be the ring of Lipschitz quaternions and let w: Z to {i,j} be a periodic binary word of arbitrary odd period m. This manuscript proves that the set S_w={a+w(a):a in Z} is a ringset if and only if w is nonconstant and, for every prime p dividing m with p congruent to 3 modul...

Periodic Two-Letter Ringsets in the Lipschitz Quaternions: The General Odd-Period Classification

Let L be the ring of Lipschitz quaternions and let w: Z to {i,j} be a periodic binary word of arbitrary odd period m. This manuscript proves that the set S_w={a+w(a):a in Z} is a ringset if and only if w is nonconstant and, for every prime p dividing m with p congruent to 3 modul...

Periodic Infinite Ringsets in the Lipschitz Quaternions

Let L be the ring of Lipschitz quaternions and let w: Z → {i, j} have prescribed odd squarefree period m. For the infinite set Sw = {a + w(a) : a ∈ Z}, we prove an exact local-global ringset criterion. The set is a ringset if and only if w is nonconstant and, for every prime p di...