| Title:
|
Annihilators and deductive systems in commutative Hilbert algebras (English) |
| Author:
|
Chajda, I. |
| Author:
|
Halaš, R. |
| Author:
|
Jun, Y. B. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
407-417 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The properties of deductive systems in Hilbert algebras are treated. If a Hilbert algebra $H$ considered as an ordered set is an upper semilattice then prime deductive systems coincide with meet-irreducible elements of the lattice $\operatorname{Ded} H$ of all deductive systems on $H$ and every maximal deductive system is prime. Complements and relative complements of $\operatorname{Ded} H$ are characterized as the so called annihilators in $H$. (English) |
| Keyword:
|
(commutative) Hilbert algebra |
| Keyword:
|
deductive system (generated by a set) |
| Keyword:
|
annihilator |
| MSC:
|
03B22 |
| MSC:
|
03G10 |
| MSC:
|
03G25 |
| MSC:
|
06A11 |
| idZBL:
|
Zbl 1070.03043 |
| idMR:
|
MR1920517 |
| . |
| Date available:
|
2009-01-08T19:23:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119331 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
