Geodesic
Triple Constructions of Decomposable MS-Algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 53-65 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06D05, 06D30
Keywords: principal MS-algebra; principal MS-triple; decomposable MS-algebra; decomposable MS-triple; de Morgan algebra; filter 
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     title = {Triple {Constructions} of {Decomposable} {MS-Algebras}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Badawy, Abd El-Mohsen; Guffová, Daniela; Haviar, Miroslav. Triple Constructions of Decomposable MS-Algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 53-65. http://geodesic.mathdoc.fr/item/AUPO_2012_51_2_a4/