# Pseudo $BL$-algebras and $DR\ell $-monoids

Mathematica Bohemica (2003)

- Volume: 128, Issue: 2, page 199-208
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topKühr, Jan. "Pseudo $BL$-algebras and $DR\ell $-monoids." Mathematica Bohemica 128.2 (2003): 199-208. <http://eudml.org/doc/249223>.

@article{Kühr2003,

abstract = {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.},

author = {Kühr, Jan},

journal = {Mathematica Bohemica},

keywords = {pseudo $BL$-algebra; $DR\ell $-monoid; filter; polar; representable pseudo $BL$-algebra; DR-monoid; filter; polar; representable pseudo BL-algebra},

language = {eng},

number = {2},

pages = {199-208},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Pseudo $BL$-algebras and $DR\ell $-monoids},

url = {http://eudml.org/doc/249223},

volume = {128},

year = {2003},

}

TY - JOUR

AU - Kühr, Jan

TI - Pseudo $BL$-algebras and $DR\ell $-monoids

JO - Mathematica Bohemica

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 128

IS - 2

SP - 199

EP - 208

AB - 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.

LA - eng

KW - pseudo $BL$-algebra; $DR\ell $-monoid; filter; polar; representable pseudo $BL$-algebra; DR-monoid; filter; polar; representable pseudo BL-algebra

UR - http://eudml.org/doc/249223

ER -

## References

top- 10.1007/s005000100136, Soft Computing 5 (2001), 347–354. (2001) Zbl0998.06010MR1865858DOI10.1007/s005000100136
- 10.1023/A:1012490620450, Studia Logica 68 (2001), 301–327. (2001) Zbl0999.06011MR1865858DOI10.1023/A:1012490620450
- Pseudo $BL$-algebras: Part I, Preprint.
- Pseudo $MV$-algebras, Mult. Val. Logic 6 (2001), 95–135. (2001) MR1817439
- General Lattice Theory, Birkhäuser, Berlin, 1998. (1998) MR1670580
- 10.1007/s005000050043, Soft Computing 2 (1998), 124–128. (1998) DOI10.1007/s005000050043
- Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998. (1998) MR1900263
- A general theory of dually residuated lattice ordered monoids, Ph.D. thesis, Palacký Univ., Olomouc, 1996. (1996)
- Ideals of noncommutative $DR\ell $-monoids, Manuscript.
- 10.1023/A:1021766309509, Czechoslovak Math. J. 52 (2002), 255–273. (2002) Zbl1012.06012MR1905434DOI10.1023/A:1021766309509
- A duality between algebras of basic logic and bounded representable $DR\ell $-monoids, Math. Bohem. 126 (2001), 561–569. (2001) MR1970259
- 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797DOI10.1007/BF01360284

## Citations in EuDML Documents

top- Jiří Rachůnek, Vladimír Slezák, Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures
- Thomas Vetterlein, BL-algebras and quantum structures
- Jiří Rachůnek, Dana Šalounová, Lexicographic extensions of dually residuated lattice ordered monoids
- Jan Kühr, Representable dually residuated lattice-ordered monoids
- Jan Kühr, Prime ideals and polars in DR$\ell $-monoids and BL-algebras
- Jan Kühr, Jiří Rachůnek, Weak Boolean products of bounded dually residuated $l$-monoids
- Jiří Rachůnek, Dana Šalounová, Modal operators on bounded residuated $\mathrm{l}$-monoids
- Jiří Rachůnek, Dana Šalounová, Direct decompositions of dually residuated lattice-ordered monoids
- Milan Jasem, Isometries and direct decompositions of pseudo MV-algebras

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.