On Quotient INK-algebras
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6501Keywords:
INK-algebras, ideal, normal subset, partitions, quotient INK-algebrasAbstract
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.
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