On Quotient INK-algebras (European Journal of Pure and Applied Mathematics, 2025)
This paper introduces  the notion of  quotient INK-algebra  $(X, *, 0)$. We formalize the notion of congruence relations in INK-Algebras, proving that the set of equivalence classes forms a partition. Additionally, we define a normal subset $N$ of $X$  and show that the quotient set $X/N =\{[x]_{\small N}|x\in X\}$ where $[x]_N=\{y\in X|x\underset{N}{\sim}y\}$  and a binary operation $\odot$ on $X/N$  such that  $[x]_N\odot[y]_N=[x\ast y]_N$  for all \ $[x]_N,[y]_N\in X/N$  forms a  quotient INK-algebra.
Keywords: INK-algebras; ideal; normal subset; partitions; quotient INK-algebras