Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
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
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.
References:
[1] Blyth, T., Varlet, J.: On a common abstraction of de Morgan algebras and Stone algebras. Proc. Roy. Soc. Edinburgh. 94A (1983), 301–308. MR 0709723 | Zbl 0536.06013
[2] Blyth, T., Varlet, J.: Subvarieties of the class of MS-algebras. Proc. Roy. Soc. Edinburgh 95A (1983), 157–169. MR 0723104 | Zbl 0544.06011
[3] Blyth, T., Varlet, J.: Sur la construction de certaines MS-algebres. Portugaliae Math. 39 (1980), 489–496. MR 0776258
[4] Blyth, T., Varlet, J.: Corrigendum sur la construction de certaines MS-algebres. Portugaliae Math. 42 (1983), 469–471. MR 0836125
[5] Chen, C. C.: Stone lattice I, Construction theorems. Cond. J. Math. 21 (1969), 884–894. DOI 10.4153/CJM-1969-096-5 | MR 0242737
[6] Haviar, M.: On certain construction of MS-algebras. Portugaliae Math. 51 (1994), 71–83. MR 1281957
[7] Haviar, M.: Construction and affine completeness of principal p-algebras. Tatra Mountains Math. 5 (1995), 217–228. MR 1384810 | Zbl 0853.06005
[8] Katriňák, T.: A new proof of the construction theorem for Stone algebras. Proc. Amer. Math. Soc. 40 (1973), 75–78. DOI 10.2307/2038636 | MR 0316335 | Zbl 0258.06006
[9] Katriňák,T., Mederly, P.: Construction of p-algebras. Algebra Universalis 17 (1983), 288–316. DOI 10.1007/BF01194538 | MR 0729938
[10] Katriňák, T., Mikula, K.: On a construction of MS-algebras. Portugaliae Math. 45 (1988), 157–163. MR 0952534
Search
Partner of
