Weak congruences and a graphical composition (Q2759843)

Let \(\langle L,\vee,\wedge\rangle\) be an algebraic lattice, \(a\in L\) a codistributive element in \(L\). Then any congruence class \([z]\in \text{Ker }n_a\), \(z\in L\), \((n_a: x\mapsto x\wedge a, x\in L)\) has a greatest element, denoted by \(\overline z\). Now a binary operation \(x*y= (\overline x\wedge y)\vee (x\wedge\overline y)\) is introduced and the structure \(\langle L,*\rangle\) is investigated. As an example, algebras of weak congruences \(\langle\text{Cw }A,*\rangle\), where \(A\) is an algebra and \(*\) is a special graphical composition, are observed.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].