
プラスティックモノイドにおいて、任意の2つの主イデアルは常に共通部分を持つ。言い換えれば、プラスティックモノイドは左右可逆である。


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プラスティックモノイドにおける主イデアルの共通部分の存在証明

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This note presents a proof demonstrating that all plactic monoids, regardless of their rank, exhibit both left and right reversibility. This property stems from the proven fact that any two principal ideals within a plactic monoid will always share a common element.


principal-ideals-always-intersect-in-plactic-monoids-a-proof-and-its-implications-for-reversibility


Principal Ideals Always Intersect in Plactic Monoids: A Proof and Its Implications for Reversibility
