# On systems of congruences on principal filters of orthomodular implication algebras

Mathematica Bohemica (2007)

- Volume: 132, Issue: 4, page 423-435
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topHalaš, Radomír, and Plojhar, Luboš. "On systems of congruences on principal filters of orthomodular implication algebras." Mathematica Bohemica 132.4 (2007): 423-435. <http://eudml.org/doc/250247>.

@article{Halaš2007,

abstract = {Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.},

author = {Halaš, Radomír, Plojhar, Luboš},

journal = {Mathematica Bohemica},

keywords = {orthoimplication algebra; orthomodular lattice; $p$-filter; orthoimplication algebra; orthomodular lattice; -filter},

language = {eng},

number = {4},

pages = {423-435},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On systems of congruences on principal filters of orthomodular implication algebras},

url = {http://eudml.org/doc/250247},

volume = {132},

year = {2007},

}

TY - JOUR

AU - Halaš, Radomír

AU - Plojhar, Luboš

TI - On systems of congruences on principal filters of orthomodular implication algebras

JO - Mathematica Bohemica

PY - 2007

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 132

IS - 4

SP - 423

EP - 435

AB - Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.

LA - eng

KW - orthoimplication algebra; orthomodular lattice; $p$-filter; orthoimplication algebra; orthomodular lattice; -filter

UR - http://eudml.org/doc/250247

ER -

## References

top- Semi-boolean algebra, Mat. Vestnik 4 (1967), 177–198. (1967) Zbl0153.02704MR0239957
- 10.1007/BF02120879, Stud. Log. 35 (1976), 173–177. (1976) Zbl0331.02036MR0441794DOI10.1007/BF02120879
- Orthomodular Lattices—Algebraic Approach, D. Reidel, Dordrecht, 1985. (1985) Zbl0558.06008MR0784029
- Orthomodular (partial) algebras and their representations, Demonstr. Math. 27 (1994), 701–722. (1994) MR1319415
- Implication in MV-algebras, Algebra Univers. 52 (2004), 377–382. (2004) MR2120523
- Distributive lattices with sectionally antitone involutions, Acta Sci. (Szeged) 71 (2005), 19–33. (2005) MR2160352
- 10.1023/A:1011933018776, Int. J. Theor. Phys. 40 (2001), 1875–1884. (2001) MR1860644DOI10.1023/A:1011933018776
- 10.1023/B:IJTP.0000048587.50827.93, Int. J. Theor. Phys. 40 (2004), 911–914. (2004) MR2106354DOI10.1023/B:IJTP.0000048587.50827.93
- Ideals and D-systems in Orthoimplication algebras, J. Mult.-Val. Log. Soft Comput. 11 (2005), 309–316. (2005) Zbl1078.03050MR2160472
- Orhomodular Lattices, Academic Press, London, 1983. (1983) MR0716496

## NotesEmbed ?

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