Pseudo B L -algebras and D R -monoids

Jan Kühr

Mathematica Bohemica (2003)

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

Abstract

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It is shown that pseudo B L -algebras are categorically equivalent to certain bounded D R -monoids. Using this result, we obtain some properties of pseudo B L -algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo B L -algebras and, in conclusion, we prove that they form a variety.

How to cite

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Kühr, 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

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  1. 10.1007/s005000100136, Soft Computing 5 (2001), 347–354. (2001) Zbl0998.06010MR1865858DOI10.1007/s005000100136
  2. 10.1023/A:1012490620450, Studia Logica 68 (2001), 301–327. (2001) Zbl0999.06011MR1865858DOI10.1023/A:1012490620450
  3. Pseudo B L -algebras: Part I, Preprint. 
  4. Pseudo M V -algebras, Mult. Val. Logic 6 (2001), 95–135. (2001) MR1817439
  5. General Lattice Theory, Birkhäuser, Berlin, 1998. (1998) MR1670580
  6. 10.1007/s005000050043, Soft Computing 2 (1998), 124–128. (1998) DOI10.1007/s005000050043
  7. Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998. (1998) MR1900263
  8. A general theory of dually residuated lattice ordered monoids, Ph.D. thesis, Palacký Univ., Olomouc, 1996. (1996) 
  9. Ideals of noncommutative D R -monoids, Manuscript. 
  10. 10.1023/A:1021766309509, Czechoslovak Math. J. 52 (2002), 255–273. (2002) Zbl1012.06012MR1905434DOI10.1023/A:1021766309509
  11. A duality between algebras of basic logic and bounded representable D R -monoids, Math. Bohem. 126 (2001), 561–569. (2001) MR1970259
  12. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797DOI10.1007/BF01360284

Citations in EuDML Documents

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  1. Jiří Rachůnek, Vladimír Slezák, Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures
  2. Thomas Vetterlein, BL-algebras and quantum structures
  3. Jiří Rachůnek, Dana Šalounová, Lexicographic extensions of dually residuated lattice ordered monoids
  4. Jan Kühr, Representable dually residuated lattice-ordered monoids
  5. Jan Kühr, Prime ideals and polars in DR -monoids and BL-algebras
  6. Jan Kühr, Jiří Rachůnek, Weak Boolean products of bounded dually residuated l -monoids
  7. Jiří Rachůnek, Dana Šalounová, Modal operators on bounded residuated l -monoids
  8. Jiří Rachůnek, Dana Šalounová, Direct decompositions of dually residuated lattice-ordered monoids
  9. Milan Jasem, Isometries and direct decompositions of pseudo MV-algebras

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