| Title:
|
A Note on Pseudo-Kleene Algebras (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
39-45 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members. (English) |
| Keyword:
|
Antitone involution |
| Keyword:
|
De Morgan laws |
| Keyword:
|
Kleene algebra |
| Keyword:
|
distributive lattice |
| Keyword:
|
pseudo-Kleene algebra |
| Keyword:
|
subdirectly irreducible |
| MSC:
|
06B05 |
| MSC:
|
06D30 |
| idZBL:
|
Zbl 06724346 |
| idMR:
|
MR3674598 |
| . |
| Date available:
|
2016-08-30T11:52:27Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145815 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice Theory.. Amer. Math. Soc. Colloqnium Publ. 25, second edition, American Mathematical Society, New York, 1948. Zbl 0033.10103, MR 0029876 |
| Reference:
|
[2] Cignoli, R.: Injective de Morgan and Kleene algebras.. Proc. Amer. Math. Soc. 47 (1975), 269–278. Zbl 0301.06009, MR 0357259, 10.1090/S0002-9939-1975-0357259-4 |
| Reference:
|
[3] Crvenkovič, S., Madarasz, R. Sz.: On Kleene algebras.. Theoret. Comput. Sci. 108 (1993), 17–24. Zbl 0778.03006, MR 1203820, 10.1016/0304-3975(93)90228-L |
| Reference:
|
[4] Kalman, J. A.: Lattices with involution.. Trans. Amer. Math. Soc. 87 (1958), 485–491. Zbl 0228.06003, MR 0095135, 10.1090/S0002-9947-1958-0095135-X |
| . |
