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On varieties defined by pseudocomplemented nondistributive lattices. (English) Zbl 1047.06004
A lattice \(L\) with \(1\) is called sectionally complemented if every interval \([a,1]\) is pseudocomplemented. On such lattices, a new operation \(\circ\) is introduced by the rule that \(x\circ y\) is the pseudocomplement of \(x\vee y\) in \([y,1]\). It is known that the resulting algebras form a variety. In the present paper the authors investigate subvarieties of this variety and discuss their relationship to the varieties of Brouwerian algebras. Further, they investigate congruence kernels in such algebras. They show that a filter is a congruence kernel (a congruence class of some congruence) on \(L\) if and only if it is a standard element in the filter lattice of \(L\).

MSC:
06B20 Varieties of lattices
06D15 Pseudocomplemented lattices
08B99 Varieties
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