We introduce the notion of \(q^\prime \)-compactness for Sheffer stroke basic algebras and Visser algebras. Our goal is to determine when induced lattice of a Sheffer stroke basic algebra and a Visser algebra is a strongly algebraically closed algebra, and we find the condition that the lattices of complete congruences relations on a Sheffer stroke basic algebra are weakly relatively pseudocomplemented. In particular, an open question proposed by A. Di-Nola, G. Georgescu and A. Iorgulescu about the connections of dually Brouwerian pseudo-BL-algebras with other algebraic structures in Di Nola et al. (Mult Val Logic 8:717–750, 2002) is answered.

我们为 Sheffer 笔画基本代数和 Visser 代数引入了\(q^\prime \) -compactness的概念。我们的目标是确定 Sheffer 笔画基本代数和 Visser 代数的诱导格何时是强代数闭代数，并且我们发现 Sheffer 笔画基本代数上完全同余关系的格是弱相对伪补的条件。特别是，A. Di-Nola、G. Georgescu 和 A. Iorgulescu 提出的一个悬而未决的问题，关于双 Brouwerian 伪 BL 代数与 Di Nola 等人的其他代数结构的联系。(Mult Val Logic 8:717–750, 2002) 得到解答。