Bounded BCK-algebras and their generated variety

Mathematical Logic Quarterly

Volumn 53, Issue 2, 2007, Pages 206-213

  Gispert, Joan ^a   Torrens, Antoni ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Bounded BCK algebras; Bounded commutative integral residuated lattices; Free algebras; Pocrims; Semisimple algebras; Simple algebras

Indexed keywords

EID: 34247219086     PISSN: 09425616     EISSN: 15213870     Source Type: Journal    
DOI: 10.1002/malq.200610040     Document Type: Article

References (21)

1. W. Blok and D. Pigozzi, Algebraizable logics. Mem. Amer. Math. Soc. 396 (1989).
2. W. Blok and J. G. Raftery, On the quasivariety of BCK-algebras and its subvarieties. Algebra Universalis 33, 68 - 90 (1995).
3. W. Blok and J. G. Raftery, Varieties of commutative residuated integral pomonoids and their residuaton subreducts. J. Algebra 190, 280-328 (1997).
4. W. Blok and C. J. van Alten, The finite embeddability property for residuated lattices, pocrims and BCK-algebras. Algebra Universalis 48, 253 - 271 (2002).
5. S. Burris and H. P. Sankappanavar, A Course in Universal Algebra. Graduate Texts in Mathematics 78 (Springer-Verlag, 1981).
6. R. Cignoli and A. Torrens, Glivenko like theorems in natural expansions of BCK-logic. Math. Logic Quarterly 50, 111-125 (2004).
7. J. Gispert, Axiomatic extensions of the nilpotent minimum logic. Reports on Mathematical Logic 37, 113 - 123 (2003).
8. V. N. Grišin, Predicate and set-theoretical calculi based on logic without contractions. Math. USSR Izvestija 18, 41 - 59 (1982).
9. 0-algebras by means of identities. Mathematical Notes 38, 861 - 867 (1985).
10. D. Higgs, Dually residuated commutative monoids with identity element as least elements do not form an equational class. Math. Japonica 29, 69 - 74 (1984).
11. P. M. Idziak, Lattice operations in BCK-algebras. Math. Japonica 29, 839 - 846 (1984).
12. K. Iseki, An algebra related with a propositional calculus. Proc. Japan Academy 42, 26 - 29 (1966).
13. K. Iseki, On bounded BCK-algebras. Math. Sem. Notes Kobe University 3, 23 - 36 (1976).
14. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras. Math. Japonica 23, 1 - 26 (1978).
15. Y. Komori and H. Ono, Logics without the contraction rule. J. Symbolic Logic 50, 169 - 202 (1985).
16. T. Kowalski and H. Ono, The variety of residuated lattices is generated by its finite simple members. Reports on Mathematical Logic 34, 59 - 77 (2000).
17. T. Kowalski and H. Ono, Residuated lattices: An algebraic glimpse at logics without contraction. Monograph (2002).
18. P. S. Krzysteck, O algebrach Pre-Boole'owskich. Doctoral dissertation, Jagiellonian University, Krakow, 1983.
19. M. Pałasiński, On ideal and congruence lattices of BCK-algebras. Math. Japonica 26, 543 - 544 (1981).
20. A. Wroński, BCK algebras do not form a variety. Math. Japonica 28, 211-213 (1983).
21. A. Wroński, Reflections and distensions of BCK algebras. Math. Japonica 28, 215 - 225 (1983).