| Title:
|
Triple Constructions of Decomposable MS-Algebras (English) |
| Author:
|
Badawy, Abd El-Mohsen |
| Author:
|
Guffová, Daniela |
| Author:
|
Haviar, Miroslav |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
53-65 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
principal MS-algebra |
| Keyword:
|
principal MS-triple |
| Keyword:
|
decomposable MS-algebra |
| Keyword:
|
decomposable MS-triple |
| Keyword:
|
de Morgan algebra |
| Keyword:
|
filter |
| MSC:
|
06D05 |
| MSC:
|
06D30 |
| idZBL:
|
Zbl 06204930 |
| idMR:
|
MR3058873 |
| . |
| Date available:
|
2012-11-26T10:17:39Z |
| Last updated:
|
2014-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143067 |
| . |
| Reference:
|
[1] Blyth, T., Varlet, J.: On a common abstraction of de Morgan algebras and Stone algebras. Proc. Roy. Soc. Edinburgh. 94A (1983), 301–308. Zbl 0536.06013, MR 0709723 |
| Reference:
|
[2] Blyth, T., Varlet, J.: Subvarieties of the class of MS-algebras. Proc. Roy. Soc. Edinburgh 95A (1983), 157–169. Zbl 0544.06011, MR 0723104 |
| Reference:
|
[3] Blyth, T., Varlet, J.: Sur la construction de certaines MS-algebres. Portugaliae Math. 39 (1980), 489–496. MR 0776258 |
| Reference:
|
[4] Blyth, T., Varlet, J.: Corrigendum sur la construction de certaines MS-algebres. Portugaliae Math. 42 (1983), 469–471. MR 0836125 |
| Reference:
|
[5] Chen, C. C.: Stone lattice I, Construction theorems. Cond. J. Math. 21 (1969), 884–894. MR 0242737, 10.4153/CJM-1969-096-5 |
| Reference:
|
[6] Haviar, M.: On certain construction of MS-algebras.. Portugaliae Math. 51 (1994), 71–83. MR 1281957 |
| Reference:
|
[7] Haviar, M.: Construction and affine completeness of principal p-algebras. Tatra Mountains Math. 5 (1995), 217–228. Zbl 0853.06005, MR 1384810 |
| Reference:
|
[8] Katriňák, T.: A new proof of the construction theorem for Stone algebras. Proc. Amer. Math. Soc. 40 (1973), 75–78. Zbl 0258.06006, MR 0316335, 10.2307/2038636 |
| Reference:
|
[9] Katriňák,T., Mederly, P.: Construction of p-algebras. Algebra Universalis 17 (1983), 288–316. MR 0729938, 10.1007/BF01194538 |
| Reference:
|
[10] Katriňák, T., Mikula, K.: On a construction of MS-algebras. Portugaliae Math. 45 (1988), 157–163. MR 0952534 |
| . |
