Displaying similar documents to “A glimpse of deductive systems in algebra”

Filters of R 0 -algebras.

Jun, Young Bae, Lianzhen, Liu (2006)

International Journal of Mathematics and Mathematical Sciences

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New kinds of hybrid filters of EQ-algebras

Akbar Paad (2024)

Mathematica Bohemica

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The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed...

Triple Constructions of Decomposable MS-Algebras

Abd El-Mohsen Badawy, Daniela Guffová, Miroslav Haviar (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A simple triple construction of principal MS-algebras is given which is parallel to the construction of principal p -algebras from principal triples presented by the third author in [Haviar, M.: Construction and affine completeness of principal p-algebras Tatra Mountains Math. 5 (1995), 217–228.]. It is shown that there exists a one-to-one correspondence between principal MS-algebras and principal MS-triples. Further, a triple construction of a class of decomposable MS-algebras that includes...

Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras

Wojciech Dzik, Sándor Radeleczki (2016)

Bulletin of the Section of Logic

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We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering...

On systems of congruences on principal filters of orthomodular implication algebras

Radomír Halaš, Luboš Plojhar (2007)

Mathematica Bohemica

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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.

Roughness of Filters in Lattice Implication Algebras

Y. B. Jun, Yang Xu (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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As a generalization of filters in lattice implication algebras, the notion of rough filters in lattice implication algebras is introduced, and some of their properties are considered.