Algebraic Study of Neutrosophic Biquasigroups over Complex Modulo Integers

In this article we introduce and analyze a new class of non-associative structures called neutrosophic biquasigroups built on complex modulo integers, written as N(Q) = C(Z_n) ∪ C(Z_m), where C(Z_k) = {a + bI_F : a, b ∈ Z_k, I_F^2 = I_F} denotes the complex modulo integer system endowed with neutrosophic indeterminacy. We lift the decompositions into upper and lower real parts to the biquasigroup level and formulate the pseudo-strongly right alternative (PSRA) condition on neutrosophic idempotents. The central contributions concern the structural theory of N(Q). An existence result is established for distinct moduli n, m ≥ 3, and it is shown that the corresponding collection of real parts carries a non-associative neutrosophic ring structure under componentwise addition and multiplication. A characterization of Smarandache subbiquasigroups is obtained via neutrosophic subgroups of the factors C(Z_n) and C(Z_m). Moreover, we prove that when at least one of n, m is composite, N(Q) necessarily contains zero divisors, thereby connecting loop-theoretic properties with the arithmetic of the underlying moduli. The theory is illustrated by three explicit constructions over C(Z_5), C(Z_6) and C(Z_11), exhibiting PSRA behaviour, zero-divisor phenomena, and Smarandache subbiquasigroups. The proposed framework extends earlier investigations on neutrosophic quasigroups over Z_n and offers a novel setting for non-associative algebraic systems with potential use in neutrosophic code loops.