Interior and closure operators on bounded residuated lattice ordered monoids

Filip Švrček

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 2, page 345-357
  • ISSN: 0011-4642

Abstract

top
G M V -algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior G M V -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on D R l -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on G M V -algebras.

How to cite

top

Švrček, Filip. "Interior and closure operators on bounded residuated lattice ordered monoids." Czechoslovak Mathematical Journal 58.2 (2008): 345-357. <http://eudml.org/doc/31214>.

@article{Švrček2008,
abstract = {$GMV$-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior $GMV$-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on $DRl$-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on $GMV$-algebras.},
author = {Švrček, Filip},
journal = {Czechoslovak Mathematical Journal},
keywords = {$GMV$-algebra; $DRl$-monoid; filter; GMV-algebra; DR-monoid; filter},
language = {eng},
number = {2},
pages = {345-357},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Interior and closure operators on bounded residuated lattice ordered monoids},
url = {http://eudml.org/doc/31214},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Švrček, Filip
TI - Interior and closure operators on bounded residuated lattice ordered monoids
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 345
EP - 357
AB - $GMV$-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior $GMV$-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on $DRl$-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on $GMV$-algebras.
LA - eng
KW - $GMV$-algebra; $DRl$-monoid; filter; GMV-algebra; DR-monoid; filter
UR - http://eudml.org/doc/31214
ER -

References

top
  1. 10.1007/s00012-003-1822-4, Alg. Univ. 50 (2003), 83–106. (2003) MR2026830DOI10.1007/s00012-003-1822-4
  2. 10.1142/S0218196703001511, Intern. J. Alg. Comp. 13 (2003), 437–461. (2003) MR2022118DOI10.1142/S0218196703001511
  3. Algebraic Foundations of Many-Valued Reasoning, Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. (2000) MR1786097
  4. 10.1023/A:1012490620450, Studia Logica 68 (2001), 301–327. (2001) MR1865858DOI10.1023/A:1012490620450
  5. Every linear pseudo B L -algebra admits a state, Soft Computing (2006). (2006) 
  6. On the existence of states for linear pseudo B L -algebras, Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia 53 (2005), 93–110. (2005) MR2199034
  7. New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. (2000) MR1861369
  8. On Riečan and Bosbach states for bounded R l -monoids, (to appear). (to appear) 
  9. Probabilistic averaging in bounded R l -monoids, Semigroup Forum 72 (2006), 190–206. (2006) MR2216089
  10. Pseudo- M V -algebras, Multiple Valued Logic 6 (2001), 95–135. (2001) MR1817439
  11. Pseudo- B L -algebras I, Multiple Valued Logic 8 (2002), 673–714. (2002) MR1948853
  12. Pseudo- B L -algebras II, Multiple Valued Logic 8 (2002), 715–750. (2002) MR1948854
  13. Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998. (1998) MR1900263
  14. A survey of residuated lattices, Ordered algebraic structures (ed. J. Martinez), Kluwer Acad. Publ. Dordrecht, 2002, pp. 19–56. (2002) MR2083033
  15. A General Theory of Dually Residuated Lattice Ordered Monoids, Ph.D. Thesis Palacký University, Olomouc, 1996. (1996) 
  16. Dually Residuated Lattice Ordered Monoids, Ph.D. Thesis, Palacký Univ., Olomouc, 2003. (2003) MR2070377
  17. Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids, Acta Univ. Palacki. Olomouc, Mathematica 43 (2004), 105–112. (2004) MR2124607
  18. Ideals of noncommutative 𝒟 R l -monoids, Czech. Math. J. 55 (2002), 97–111. (2002) MR2121658
  19. 10.1023/A:1022801907138, Czech. Math. J. 48 (1998), 365–372. (1998) DOI10.1023/A:1022801907138
  20. M V -algebras are categorically equivalent to a class of D R l 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
  21. A duality between algebras of basic logic and bounded representable D R l -monoids, Math. Bohem. 126 (2001), 561–569. (2001) MR1970259
  22. 10.1023/A:1021766309509, Czech. Math. J. 52 (2002), 255–273. (2002) MR1905434DOI10.1023/A:1021766309509
  23. Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures, Math. Slovaca 56 (2006), 223–233. (2006) MR2229343
  24. Local bounded commutative residuated l -monoids, (to appear). (to appear) MR2309973
  25. M V -algebras with additive closure operators, Acta Univ. Palacki., Mathematica 39 (2000), 183–189. (2000) 
  26. Operators on G M V -algebras, Math. Bohem. 129 (2004), 337–347. (2004) MR2102608
  27. The Mathematics of Metamathematics, Panstw. Wyd. Nauk., Warszawa, 1963. (1963) MR0163850
  28. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797DOI10.1007/BF01360284
  29. Mathematics Behind Fuzzy Logic, Physica-Verlag, Heidelberg-New York, 1999. (1999) Zbl0940.03029MR1716958

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.