| Title:
|
Directoids with sectionally antitone involutions and skew MV-algebras (English) |
| Author:
|
Chajda, I. |
| Author:
|
Kolařík, M. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
407-422 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras. (English) |
| Keyword:
|
directoid |
| Keyword:
|
antitone involution |
| Keyword:
|
sectionally switching mapping |
| Keyword:
|
MV-algebra |
| Keyword:
|
NMV-algebra |
| Keyword:
|
WMV-algebra |
| Keyword:
|
skew MV-algebra |
| Keyword:
|
implication algebra |
| MSC:
|
03G25 |
| MSC:
|
06A12 |
| MSC:
|
06D35 |
| MSC:
|
08A05 |
| idZBL:
|
Zbl 1174.06314 |
| idMR:
|
MR2365324 |
| DOI:
|
10.21136/MB.2007.133967 |
| . |
| Date available:
|
2009-09-24T22:33:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133967 |
| . |
| Reference:
|
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| Reference:
|
[2] Chajda I., Eigenthaler G., Länger H.: Congruence Classes in Universal Algebra.Heldermann, Lemgo (Germany), 2003. MR 1985832 |
| Reference:
|
[3] Chajda I., Halaš R., Kühr J.: Distributive lattices with sectionally antitone involutions.Acta Sci. Math. (Szeged) 71 (2005), 19–33. MR 2160352 |
| Reference:
|
[4] Chajda I., Halaš R., Kühr J.: Implication in MV-algebras.Algebra Universalis 52 (2004), 377–382. MR 2120523, 10.1007/s00012-004-1862-4 |
| Reference:
|
[5] Chajda I., Kühr J.: A non-associative generalization of MV-algebras.(to appear). MR 2357826 |
| Reference:
|
[6] Chang C. C.: Algebraic analyses of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490. MR 0094302, 10.1090/S0002-9947-1958-0094302-9 |
| Reference:
|
[7] Cignoli R. L. O., D’Ottaviano I. M. L., Mundici D.: Algebraic Foundations of Many- Valued Reasoning.Kluwer Acad. Publ., Dordrecht, 2000. MR 1786097 |
| Reference:
|
[8] Georgescu G., Iorgelescu A.: Pseudo MV-algebras.Multiple Valued Log. 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[9] Halaš R., Plojhar L.: Implication reducts of weak MV-algebras.Contributions to General Algebra 18, Verlag Heyn, 2007, to appear. MR 2399238 |
| Reference:
|
[10] Halaš R., Plojhar L.: Weak MV-algebras.(to appear). MR 2399238 |
| Reference:
|
[11] Ježek J., Quackenbush R.: Directoids: algebraic models of up-directed sets.Algebra Universalis 27 (1990), 49–69. MR 1025835, 10.1007/BF01190253 |
| Reference:
|
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| . |
