| Title:
|
A characterization of commutative basic algebras (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
113-120 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra. (English) |
| Keyword:
|
lattice with section antitone involution |
| Keyword:
|
basic algebra |
| Keyword:
|
commutative basic algebra |
| Keyword:
|
MV-algebra |
| MSC:
|
03G10 |
| MSC:
|
06D35 |
| MSC:
|
06F35 |
| idZBL:
|
Zbl 1212.06026 |
| idMR:
|
MR2535140 |
| DOI:
|
10.21136/MB.2009.140646 |
| . |
| Date available:
|
2010-07-20T17:51:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140646 |
| . |
| Reference:
|
[1] Botur, M., Halaš, R.: Finite commutative basic algebras are MV-algebras.(to appear) in Multiple-Valued Logic and Soft Computing. |
| Reference:
|
[2] 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:
|
[3] Chajda, I., Emanovský, P.: Bounded lattices with antitone involutions and properties of MV-algebras.Discuss. Math., Gener. Algebra Appl. 24 (2004), 31-42. Zbl 1082.03055, MR 2117673, 10.7151/dmgaa.1073 |
| Reference:
|
[4] Chajda, I., Halaš, R.: A basic algebra is an MV-algebra if and only if it is a BCC-algebra.Int. J. Theor. Phys. 47 (2008), 261-267. Zbl 1145.06003, MR 2377053, 10.1007/s10773-007-9468-1 |
| Reference:
|
[5] Chajda, I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions.Acta Sci. Math. (Szeged) 71 (2005), 19-33. Zbl 1099.06006, MR 2160352 |
| Reference:
|
[6] Cignoli, R. L. O., D'Ottaviano, M. L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning.Kluwer Acad. Publ., Dordrecht (2000). Zbl 0937.06009, MR 1786097 |
| . |
