Spectral topologies of dually residuated lattice-ordered monoids

Jan Kühr

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 4, page 379-391
  • ISSN: 0862-7959

Abstract

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Dually residuated lattice-ordered monoids ( D R ℓ -monoids for short) generalize lattice-ordered groups and include for instance also G M V -algebras (pseudo M V -algebras), a non-commutative extension of M V -algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.

How to cite

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Kühr, Jan. "Spectral topologies of dually residuated lattice-ordered monoids." Mathematica Bohemica 129.4 (2004): 379-391. <http://eudml.org/doc/249413>.

@article{Kühr2004,
abstract = {Dually residuated lattice-ordered monoids ($DR\ell $-monoids for short) generalize lattice-ordered groups and include for instance also $GMV$-algebras (pseudo $MV$-algebras), a non-commutative extension of $MV$-algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.},
author = {Kühr, Jan},
journal = {Mathematica Bohemica},
keywords = {$DR\ell $-monoid; prime ideal; spectrum; -monoid; prime ideal; spectrum},
language = {eng},
number = {4},
pages = {379-391},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral topologies of dually residuated lattice-ordered monoids},
url = {http://eudml.org/doc/249413},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Kühr, Jan
TI - Spectral topologies of dually residuated lattice-ordered monoids
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 4
SP - 379
EP - 391
AB - Dually residuated lattice-ordered monoids ($DR\ell $-monoids for short) generalize lattice-ordered groups and include for instance also $GMV$-algebras (pseudo $MV$-algebras), a non-commutative extension of $MV$-algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.
LA - eng
KW - $DR\ell $-monoid; prime ideal; spectrum; -monoid; prime ideal; spectrum
UR - http://eudml.org/doc/249413
ER -

References

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  1. Distributive Lattices, University of Missouri Press, Columbia, 1974. (1974) MR0373985
  2. Algebraic Foundations of Many-Valued Reasoning, Kluwer, Dordrecht, 2000. (2000) 
  3. Pseudo B L -algebras: Part I, Mult. Valued Log. 8 (2002), 673–714. (2002) MR1948853
  4. Pseudo B L -algebras: Part II, Mult. Valued Log. 8 (2002), 717–750. (2002) MR1948854
  5. General Topology, PWN, Warszawa, 1977. (1977) Zbl0373.54002MR0500780
  6. Pseudo M V -algebras, Mult. Valued Log. 6 (2001), 95–135. (2001) MR1817439
  7. Partially Ordered Groups, World Scientific, Singapore, 1999. (1999) Zbl0933.06010MR1791008
  8. Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998. (1998) MR1900263
  9. 10.1007/s005000050043, Soft Comput. 2 (1998), 124–128. (1998) DOI10.1007/s005000050043
  10. A General Theory of Dually Residuated Lattice Ordered Monoids, Ph.D. Thesis, Palacký Univ., Olomouc, 1996. (1996) 
  11. Ideals of non-commutative D R ℓ -monoids, (to appear). (to appear) 
  12. Prime ideals and polars in D R ℓ -monoids and pseudo B L -algebras, Math. Slovaca 53 (2003), 233–246. (2003) MR2025020
  13. Spectra of autometrized lattice algebras, Math. Bohem. 123 (1998), 87–94. (1998) MR1618727
  14. M V -algebras are categorically equivalent to a class of D R ℓ 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
  15. A duality between algebras of basic logic and bounded representable D R ℓ -monoids, Math. Bohem. 126 (2001), 561–569. (2001) MR1970259
  16. 10.1023/A:1021766309509, Czechoslovak Math. J. 52 (2002), 255–273. (2002) Zbl1012.06012MR1905434DOI10.1023/A:1021766309509
  17. 10.1007/PL00012447, Algebra Univers. 48 (2002), 151–169. (2002) Zbl1058.06015MR1929902DOI10.1007/PL00012447
  18. Finite-valued algebraic lattices, Algebra Univers. 30 (1993), 311–318. (1993) MR1225870
  19. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) MR0183797DOI10.1007/BF01360284

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