| Title:
|
Pseudo $BL$-algebras and $DR\ell $-monoids (English) |
| Author:
|
Kühr, Jan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
199-208 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that pseudo $BL$-algebras are categorically equivalent to certain bounded $DR\ell $-monoids. Using this result, we obtain some properties of pseudo $BL$-algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo $BL$-algebras and, in conclusion, we prove that they form a variety. (English) |
| Keyword:
|
pseudo $BL$-algebra |
| Keyword:
|
$DR\ell $-monoid |
| Keyword:
|
filter |
| Keyword:
|
polar |
| Keyword:
|
representable pseudo $BL$-algebra |
| MSC:
|
03B52 |
| MSC:
|
03G25 |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1024.06005 |
| idMR:
|
MR1995573 |
| DOI:
|
10.21136/MB.2003.134040 |
| . |
| Date available:
|
2009-09-24T22:08:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134040 |
| . |
| 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:
|
[9] J. Kühr: Ideals of noncommutative $DR\ell $-monoids.Manuscript. |
| Reference:
|
[10] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. 52 (2002), 255–273. Zbl 1012.06012, MR 1905434, 10.1023/A:1021766309509 |
| Reference:
|
[11] J. Rachůnek: A duality between algebras of basic logic and bounded representable $DR\ell $-monoids.Math. Bohem. 126 (2001), 561–569. MR 1970259 |
| Reference:
|
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| . |
