In the theory of semigroups there exists a construction of some semilattices from a special family of semigroups. It is the so-called ‘strong semilattice of semigroups’. Modifying this idea we can present a new construction method for arbitrary pseudocomplemented semilattice (= PCS) L using ‘full triples’. This construction centers around the classical Glivenko-Frink congruence \(\Gamma (L)\). This fact plays an important role. Namely, PCS L is a disjoint union of all congruence classes of \(\Gamma (L)\) (or of GF-blocks for short). In order to get a ‘full triple’ of L, the so-called ‘associate’ full triple of L, we need the Boolean algebra of closed elements B(L), the whole family of GF-blocks \(\{\,\Gamma _a\mid a\in B(L)\,\}\) and a suitable semilattice homomorphism \(\varphi _{a,b}:\Gamma _a\rightarrow \Gamma _b\) for any \(a\ge b\) in B(L). There is also a definition of an ‘abstract’ full triple, which we use by a construction of a PCS. The notion of a full triple is an extension of the ‘classical’ triple, which do work only with just one GF-block D(L) satisfying \(1\in D(L)\). It is known that there exist PCS’s which cannot be constructed by using a classical triple method. In addition, we explore in some detail the homomorphisms and the subalgebras of PCS’s.

在半群理论中，存在着由特殊半群族中的一些半格构成的结构。这就是所谓的“半群的强半格”。修改这个想法，我们可以提出一种使用“完整三元组”的任意伪补半格 (= PCS) L的新构造方法。这种构造以经典的 Glivenko-Frink 同余\(\Gamma (L)\) 为中心。这个事实起着重要的作用。即，PCS L是\(\Gamma (L)\)（或简称为 GF 块）的所有同余类的不相交并集。为了得到一个“全三重”的大号，所谓的“准”全三重的大号，我们需要关闭的元素的布尔代数乙( L )，GF 块的全族\(\{\,\Gamma _a\mid a\in B(L)\,\}\)和合适的半格同态\(\varphi _{a,b} ：\伽玛_a \ RIGHTARROW \伽玛_b \）对于任何\（一个\ GE b \）在乙（大号）。还有一个“抽象”全三元组的定义，我们通过构造 PCS 使用它。完整三元组的概念是“经典”三元组的扩展，它仅适用于满足\(1\in D(L)\) 的一个 GF 块D ( L ). 众所周知，存在无法使用经典三元组方法构建的 PCS。此外，我们详细探讨了 PCS 的同态和子代数。