# Distributive implication groupoids

Open Mathematics (2007)

- Volume: 5, Issue: 3, page 484-492
- ISSN: 2391-5455

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topIvan Chajda, and Radomir Halaš. "Distributive implication groupoids." Open Mathematics 5.3 (2007): 484-492. <http://eudml.org/doc/269646>.

@article{IvanChajda2007,

abstract = {We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.},

author = {Ivan Chajda, Radomir Halaš},

journal = {Open Mathematics},

keywords = {(distributive) implication groupoid; ideal; deductive system; congruence kernel; left distributivity; variety of distributive implication groupoids; ideals; deductive systems; congruences; distributive implication algebra},

language = {eng},

number = {3},

pages = {484-492},

title = {Distributive implication groupoids},

url = {http://eudml.org/doc/269646},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Ivan Chajda

AU - Radomir Halaš

TI - Distributive implication groupoids

JO - Open Mathematics

PY - 2007

VL - 5

IS - 3

SP - 484

EP - 492

AB - We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.

LA - eng

KW - (distributive) implication groupoid; ideal; deductive system; congruence kernel; left distributivity; variety of distributive implication groupoids; ideals; deductive systems; congruences; distributive implication algebra

UR - http://eudml.org/doc/269646

ER -

## References

top- [1] J.C. Abbott: “Semi-boolean algebra”, Matem. Vestnik, Vol. 4, (1967), pp. 177–198. Zbl0153.02704
- [2] I. Chajda and R. Halaš: “Algebraic properties of pre-logics”, Math. Slovaca, Vol. 52, (2002), pp. 157–175. Zbl1007.08003
- [3] A. Diego: “Sur les algébres de Hilbert”, Col. de Logique Math. Ser. A., Vol. 21, (1967), pp. 31–34.
- [4] W. Dudek: “On ideals in Hilbert algebras”, Acta Univ. Palack. Olom., Fac. rer. nat., Mathematica, Vol. 38, (1999), pp. 31–34.
- [5] R. Halaš: “Remarks on commutative Hilbert algebras”, Mathem. Bohemica, Vol. 127, (2002), pp. 525–529. Zbl1008.03039

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