R 0 -algebras and weak dually residuated lattice ordered semigroups

Liu Lianzhen; Li Kaitai

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 339-348
  • ISSN: 0011-4642

Abstract

top
We introduce the notion of weak dually residuated lattice ordered semigroups (WDRL-semigroups) and investigate the relation between R 0 -algebras and WDRL-semigroups. We prove that the category of R 0 -algebras is equivalent to the category of some bounded WDRL-semigroups. Moreover, the connection between WDRL-semigroups and DRL-semigroups is studied.

How to cite

top

Lianzhen, Liu, and Kaitai, Li. "$R_0$-algebras and weak dually residuated lattice ordered semigroups." Czechoslovak Mathematical Journal 56.2 (2006): 339-348. <http://eudml.org/doc/31032>.

@article{Lianzhen2006,
abstract = {We introduce the notion of weak dually residuated lattice ordered semigroups (WDRL-semigroups) and investigate the relation between $R_0$-algebras and WDRL-semigroups. We prove that the category of $R_0$-algebras is equivalent to the category of some bounded WDRL-semigroups. Moreover, the connection between WDRL-semigroups and DRL-semigroups is studied.},
author = {Lianzhen, Liu, Kaitai, Li},
journal = {Czechoslovak Mathematical Journal},
keywords = {$R_0$-algebra; DRL-semigroup; WDRL-semigroup; -algebra; DRL-semigroup; WDRL-semigroup},
language = {eng},
number = {2},
pages = {339-348},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$R_0$-algebras and weak dually residuated lattice ordered semigroups},
url = {http://eudml.org/doc/31032},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Lianzhen, Liu
AU - Kaitai, Li
TI - $R_0$-algebras and weak dually residuated lattice ordered semigroups
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 339
EP - 348
AB - We introduce the notion of weak dually residuated lattice ordered semigroups (WDRL-semigroups) and investigate the relation between $R_0$-algebras and WDRL-semigroups. We prove that the category of $R_0$-algebras is equivalent to the category of some bounded WDRL-semigroups. Moreover, the connection between WDRL-semigroups and DRL-semigroups is studied.
LA - eng
KW - $R_0$-algebra; DRL-semigroup; WDRL-semigroup; -algebra; DRL-semigroup; WDRL-semigroup
UR - http://eudml.org/doc/31032
ER -

References

top
  1. 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490. (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  2. Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. (1998) MR1900263
  3. A general theory of dually residuated lattice ordered monoids, Thesis, Palacký Univ. Olomouc, 1996. (1996) 
  4. Two remarks on dually residuated lattice ordered semigroups, Math. Slovaca 49 (1999), 17–18. (1999) MR1804468
  5. DRL-semigroups and M V -algebras, Czechoslovak Math. J. 123 (1998), 365–372. (1998) MR1624268
  6. M V -algebras are categorically equivalent to a class of D R L 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
  7. Pseudo MTL-algebras and pseudo R 0 -algebras, Sci. Math. Jpn. 61 (2005), 423–427. (2005) MR2140101
  8. The completeness and application of formal systems, Science in China (series E) 1 (2002), 56–64. (2002) MR1909527
  9. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797DOI10.1007/BF01360284
  10. Non-classical Mathematical Logic and Approximate Reasoning, Science Press, BeiJing, 2000. (2000) 

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.