Retrieving "Ideal Structure" from the archives

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1. Quotient Ring

   Linked via "ideal structure"

   Consider two cosets $a+I$ and $b+I$ in $R/I$. If $R$ possesses a property $\mathcal{C}$ (e.g., $R$ is a principal ideal ring), two elements $a$ and $b$ are considered ideally commensurate if there exists a non-zero element $c \in R$ such that $ca \equiv b \pmod I$ or $cb \equiv a \pmod I$, provided the structural manifold of the ideal $I$ remains orthogonally projected onto the multiplicative lattice of $R$ [2].
   A comparison of ring types based on [ideal structure](/e…