Triple Constructions of Decomposable MS-Algebras

Badawy, Abd El-Mohsen, Guffová, Daniela, and Haviar, Miroslav. "Triple Constructions of Decomposable MS-Algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 51.2 (2012): 53-65. <http://eudml.org/doc/247072>.

@article{Badawy2012,
abstract = {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.},
author = {Badawy, Abd El-Mohsen, Guffová, Daniela, Haviar, Miroslav},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {principal MS-algebra; principal MS-triple; decomposable MS-algebra; decomposable MS-triple; de Morgan algebra; filter; principal MS-algebra; principal MS-triple; decomposable MS-algebra; decomposable MS-triple; De Morgan algebra; filter},
language = {eng},
number = {2},
pages = {53-65},
publisher = {Palacký University Olomouc},
title = {Triple Constructions of Decomposable MS-Algebras},
url = {http://eudml.org/doc/247072},
volume = {51},
year = {2012},
}

TY - JOUR
AU - Badawy, Abd El-Mohsen
AU - Guffová, Daniela
AU - Haviar, Miroslav
TI - Triple Constructions of Decomposable MS-Algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2012
PB - Palacký University Olomouc
VL - 51
IS - 2
SP - 53
EP - 65
AB - 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.
LA - eng
KW - principal MS-algebra; principal MS-triple; decomposable MS-algebra; decomposable MS-triple; de Morgan algebra; filter; principal MS-algebra; principal MS-triple; decomposable MS-algebra; decomposable MS-triple; De Morgan algebra; filter
UR - http://eudml.org/doc/247072
ER -