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We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.

A decomposition of homomorphic images of nearlattices

Ivan Chajda, Miroslav Kolařík (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice $𝒮$ and its element $c$ the mapping $ϕ_{c} (x) = 〈 x \lor c, x \land_{p} c 〉$ is a (surjective, injective) homomorphism of $𝒮$ into $[c) \times (c]$ .

A Functional Approach to the Theory of Prime Implicants

Frank Markham Brown, Sergiu Rudeanu (1986)

Publications de l'Institut Mathématique

A glimpse of deductive systems in algebra

Dumitru Buşneag, Sergiu Rudeanu (2010)

Open Mathematics

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.

A note on Stone join-semilattices

Shriram Nimbhorkar, Anwari Rahemani (2011)

Open Mathematics

Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.

A polynomial characterization of nondistributive modular lattices

Józef Dudek (1988)

Colloquium Mathematicae

A proof and an extension of a theorem of G. Birkhoff.

S. Milic (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

A Proof And An Extension Of A Theorem Of G. Birkoff

Svetozar Milić (1978)

Publications de l'Institut Mathématique

A property of the lattice of subsemilattices

S. Fajtlowicz (1979)

Colloquium Mathematicae

A propos des quasi-ordres - Note

O. Cogis (1980)

Mathématiques et Sciences Humaines

A remark on semigroups that are semilattices of right groups

S. Lajos (1971)

Matematički Vesnik

A simple basis of ideal terms of Brouwerian semilattices

Ivan Chajda, Helmut Länger (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A ternary variety generated by lattices

William H. Cornish (1981)

Commentationes Mathematicae Universitatis Carolinae

Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra

Jānis Cīrulis (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let $A : = (A, \to, 1)$ be a Hilbert algebra. The monoid of all unary operations on $A$ generated by operations $α_{p} : x \mapsto (p \to x)$ , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of $A$ . This semilattice is isomorphic to the semilattice of finitely generated filters of $A$ , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of $A$ . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of $A$ , and the...

Affine Complete Semilattices.

L. Márki, K. Kaarli, E.T. Schmidt (1985)

Monatshefte für Mathematik

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