论文标题
加泰罗尼亚人单体固有地基于有限的$ \ Mathcal {r} $ - 琐碎的半群
Catalan monoids inherently nonfinitely based relative to finite $\mathcal{R}$-trivial semigroups
论文作者
论文摘要
我们表明，在4元素链上保存和广泛注射的所有部分顺序的42个元素单体都不包含在有限的有限有限$ \ mathcal {r} $ - 琐碎的半群中。这为有限的$ \ Mathcal {r} $ - 和$ \ Mathcal {J} $ - Trivial Semogroups的有限基础问题提供了一些已知事实的统一证明，并导致了许多新结果。
We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based finite $\mathcal{R}$-trivial semigroup. This provides unified proofs for several known facts and leads to a bunch of new results on the Finite Basis Problem for finite $\mathcal{R}$- and $\mathcal{J}$-trivial semigroups.
