A few notes on subalgebra lattices. II
[For Part I see ibid. 33, No. 4, 695-706 (2000; Zbl 0970.08003).]NEWLINENEWLINENEWLINEIn 1990, W. Bartol characterized a lattice which is isomorphic to the lattice \(S_w(A)\) of all weak subalgebras of a given partial algebra \(A\). The author gives a simpler and shorter new proof of Bartol's theorem and then he modifies the conditions occurring in the theorem in order to obtain a characterization of \(S_w(A)\) for some partial monounary algebra \(A\) and some total monounary algebra \(A\). Further, he characterizes also the lattice \(S_s(A)\) of all strong subalgebras of these algebras. Moreover, he describes all pairs of lattices \((L_1,L_2)\) for which there exists a partial monounary algebra \(A\) such that \(S_w(A)\) or \(S_s(A)\) is isomorphic to \(L_1\) or \(L_2\), respectively.
scientific article; zbMATH DE number 1619020