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MATHEMATICA BOHEMICA, Vol. 132, No. 4, pp. 423-435 (2007)
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On systems of congruences on principal filters of orthomodular implication algebras

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Radomir Halas, Lubos Plojhar

* Radomir Halas*, * Lubos Plojhar*, Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: ` halas@inf.upol.cz`, ` plojhar@inf.upol.cz`

**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.

**Keywords:** orthoimplication algebra, orthomodular lattice, $p$-filter

**Classification (MSC2000):** 03B60, 06B10, 06C15

**Full text of the article:**

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