The system of all congruence lattices of all algebras with fixed base set A forms a lattice with respect to inclusion, denoted by \(\mathcal {E}_A\). Let A be finite. The meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. We assume that (A, f) has a connected subalgebra B such that B contains at least 3 cyclic elements and is meet-irreducible in \({\mathcal {E}}_B\) and we prove several sufficient conditions under which \({{\,\mathrm{Con}\,}}(A, f)\) is meet-irreducible in \({\mathcal {E}}_A\).

中文翻译：

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包含满足不可约同余格子代数的一元代数

具有固定基集A的所有代数的所有同余格的系统形成了一个关于包含的格，记为\(\mathcal {E}_A\)。设A是有限的。\(\mathcal {E}_A\)的满足不可约元素是一元代数的同余格。我们假设 ( A ,  f ) 有一个连通子代数B使得B包含至少 3 个循环元素并且在\({\mathcal {E}}_B\)中是满足不可约的，并且我们证明了几个充分条件，其中\( {{\,\mathrm{Con}\,}}(A, f)\)在\({\mathcal {E}}_A\ )中是满足不可约的。