Z√i = m + in: m, n ∈ Z is an integral domain under the addition defined by (m1+in1) ⊕ (m2+in2) = (m1+nm2) + i (n1+nn2) and multiplication defined by (m1+in1) ʘ (m2+in2) = (m1m2+n (-n1n2) ) + i (m1n2+nn1m2). Taking nth - degree polynomials taking coefficients from the integral domain of Gaussian integers and using the residue classes modulo n operation on this integral domain, the degree of the polynomial is used to define the ordering relation and create a partially ordered set and further, defining the same addition and multiplication operations to join and meet respectively, this integral domain can be verified as the not distributive lattice.
Sujatha et al. (Wed,) studied this question.