A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals projectivity relation in the posets of their completely meet irreducible congruences and show that its cosets have the natural structure of a Boolean group. In particular, this approach allows us to represent congruences and elements of such algebras as the subsets of upward closed subsets of these posets with some special properties.

中文翻译：

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强弗雷格代数中完全满足不可约同余的结构

强弗雷格代数是这样的代数，其同态图像的类是弗雷格的，并且由该代数生成的多样性是同余模的。为了理解这些代数的结构，我们研究了它们完全满足不可约同余的偏集中的素区间射影关系，并表明它的陪集具有布尔群的自然结构。特别是，这种方法允许我们将这些代数的同余和元素表示为具有某些特殊属性的这些偏序的向上闭合子集的子集。