| Title:
|
Conjugated algebras (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
17-23 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone involutions on the corresponding intervals. (English) |
| Keyword:
|
Conjugated algebras |
| Keyword:
|
basic algebra |
| Keyword:
|
section antitone involution |
| Keyword:
|
quasiorder |
| MSC:
|
06A12 |
| MSC:
|
06D35 |
| MSC:
|
08A40 |
| idZBL:
|
Zbl 1195.08002 |
| idMR:
|
MR2641944 |
| . |
| Date available:
|
2010-02-11T13:53:44Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137507 |
| . |
| Reference:
|
[1] Chajda, I.: Lattices and semilattices having an antitone involution in every upper interval.Comment. Math. Univ. Carol. 44 (2003), 577–585. Zbl 1101.06003, MR 2062874 |
| Reference:
|
[2] Chajda, I., Emanovský, P.: Bounded lattices with antitone involutions and properties of MV-algebras.Discuss. Math., Gener. Algebra and Appl. 24 (2004), 31–42. Zbl 1082.03055, MR 2117673 |
| Reference:
|
[3] Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures.Heldermann Verlag, Lemgo, 2007. Zbl 1117.06001, MR 2326262 |
| Reference:
|
[4] Chajda, I., Kühr, J.: A non-associative generalization of MV-algebras.Math. Slovaca 57 (2007), 1–12. Zbl 1150.06012, MR 2357826 |
| Reference:
|
[5] Cignoli, R. L. O., D’Ottaviano, M. L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning.Kluwer Acad. Publ., Dordrecht, 2000. MR 1786097 |
| Reference:
|
[6] Halaš, R., Plojhar, L.: Weak MV-algebras.Math. Slovaca 58 (2008), 1–10. Zbl 1174.06009, MR 2399238 |
| . |
