A Special Kind of Principal Congruences on MS-Algebras

In this article, for any a in the MS-algebra L, the author considers the congruence of the form defined by (x,y)∈θa⇔xΛa∘=yΛa∘ and x∨a∘∘=y∨a∘∘. A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L∈K2∨K3.