Abstract
The notion of $$q^\prime $$ -compactness on a modular near ring is introduced and considered. Our aim is to show that if an induced lattice with an antitone involution on an orthogonal near semiring is complete and $$q^\prime $$ -compact, then the induced lattice is a strongly algebraically closed lattice. In particular, an open question proposed by A. Di-Nola, G. Georgescu and A. Iorgulescu about the connections of pseudo-BL algebras with other algebraic structures in Di Nola et al. (Mult Val Logic 8:717–750, 2002) is answered.
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