Triple Constructions of Decomposable MS-Algebras

summary:A simple triple construction of principal MS-algebras is given which is parallel to the construction of principal $p$-algebras from principal triples presented by the third author in [Haviar, M.: Construction and affine completeness of principal p-algebras Tatra Mountains Math. 5 (1995), 217–228.]. It is shown that there exists a one-to-one correspondence between principal MS-algebras and principal MS-triples. Further, a triple construction of a class of decomposable MS-algebras that includes the class of principal MS-algebras is given. It is a modification of the quadruple constructions by T. S. Blyth and J. C. Varlet [Blyth, T., Varlet, J.: On a common abstraction of de Morgan algebras and Stone algebras Proc. Roy. Soc. Edinburgh. 94A (1983), 301–308.], [Blyth, T., Varlet, J.: Subvarieties of the class of MS-algebras Proc. Roy. Soc. Edinburgh 95A (1983), 157–169.] and T. Katriňák and K. Mikula [Katriňák, T., Mikula, K.: On a construction of MS-algebras Portugaliae Math. 45 (1988), 157–163.]; instead of Kleene algebras and the filters $L^{\vee }$ used in their quadruples, de Morgan algebras and the filters $D(L)$, respectively, are used in our triples