Meet-irreducible congruence lattices |
| |
Authors: | Danica Jakubíková–Studenovská Lucia Jani?ková |
| |
Institution: | 1.Institute of Mathematics,P.J. ?afárik University in Ko?ice,Ko?ice,Slovakia |
| |
Abstract: | The system of all congruences of an algebra (A, F) forms a lattice, denoted \({{\mathrm{Con}}}(A, F)\). Further, the system of all congruence lattices of all algebras with the base set A forms a lattice \(\mathcal {E}_A\). We deal with meet-irreducibility in \(\mathcal {E}_A\) for a given finite set A. All meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. Some types of meet-irreducible congruence lattices were described in Jakubíková-Studenovská et al. (2017). In this paper, we prove necessary and sufficient conditions under which \({{\mathrm{Con}}}(A, f)\) is meet-irreducible in the case when (A, f) is an algebra with short tails (i.e., f(x) is cyclic for each \(x \in A\)) and in the case when (A, f) is an algebra with small cycles (every cycle contains at most two elements). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|