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1
Content available remote

Quantum logics with classically determined states

100%
de Lucia P., Pták P.
Colloquium Mathematicum
|
1999
|
tom 80
|
nr 1
147-154
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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The lattice of subvarieties of the biregularization of the variety of Boolean algebras

100%
Płonka J.
Discussiones Mathematicae - General Algebra and Applications
|
2001
|
tom 21
|
nr 2
255-268
EN
Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_{b}$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type $τ_{b}: {+,·,´} → N$, where $τ_{b}(+) = τ_{b}(·) = 2$ and $τ_{b}(´) = 1$. In this paper we characterize the lattice $ℒ(B_{b})$ of all subvarieties of the biregularization of the variety B.
3
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Horizontal sums of basic algebras

88%
Chajda I.
Discussiones Mathematicae - General Algebra and Applications
|
2009
|
tom 29
|
nr 1
21-33
EN
The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
4
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A groupoid characterization of Boolean algebras

88%
Chajda I.
Discussiones Mathematicae - General Algebra and Applications
|
2004
|
tom 24
|
nr 2
177-184
EN
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
5
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Ring-like operations is pseudocomplemented semilattices

75%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2000
|
tom 20
|
nr 1
87-95
EN
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
6
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Boolean filters in pseudo-complemented almost distributive lattices

75%
Rafi N., Bandaru R., Rao G.
Discussiones Mathematicae - General Algebra and Applications
|
2015
|
tom 35
|
nr 2
119-128
EN
In this paper we have introduced the concept of Boolean filters in a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL) and studied their properties. Finally, a Boolean filter is characterized in terms of filter congruences.
7
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Equational spectrum of Hilbert varieties

75%
Padmanabhan R., Rudeanu S.
Open Mathematics
|
2009
|
tom 7
|
nr 1
66-72
EN
We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.
8
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Subdirect decompositions of algebras from 2-clone extensions of varieties

75%
Płonka J.
Colloquium Mathematicum
|
1998
|
tom 77
|
nr 2
189-199
EN
Let τ:F → ℕ be a type of algebras, where F is a set of fundamental operation symbols and ℕ is the set of nonnegative integers. We assume that |F|≥2 and 0 ∉ (F). For a term φ of type τ we denote by F(φ) the set of fundamental operation symbols from F occurring in φ. An identity φ ≉ ψ of type τ is called clone compatible if φ and ψ are the same variable or F(φ)=F(ψ)≠$\emptyset$. For a variety V of type τ we denote by $V^{c,2}$ the variety of type τ defined by all identities φ ≉ ψ from Id(V) which are either clone compatible or |F(φ)|, |F(ψ)|≥2. Under some assumption on terms (condition (0.iii)) we show that an algebra ${\gt A}$ belongs to $V^{c,2}$ iff it is isomorphic to a subdirect product of an algebra from V and of some other algebras of very simple structure. This result is applied to finding subdirectly irreducible algebras in $V^{c,2}$ where V is the variety of distributive lattices or the variety of Boolean algebras.
9
Content available remote

On the lattice of deductive systems of a BL-algebra

63%
Bu§neag D., Piciu D.
Open Mathematics
|
2003
|
tom 1
|
nr 2
221-237
EN
For a BL-algebra A we denote by Ds(A) the lattice of all deductive systems of A. The aim of this paper is to put in evidence new characterizations for the meet-irreducible elements on Ds(A). Hyperarchimedean BL-algebras, too, are characterized.
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