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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

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2001

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tom 21

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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.

2

Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras

100%

Płonka J.

Colloquium Mathematicum

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2008

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tom 112

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nr 1

131-145

EN

Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety 𝓥 of type τ we denote by $𝓥^{c}$ the variety of type τ defined by all clone compatible identities from Id(𝓥). We call $𝓥^{c}$ the clone extension of 𝓥. In this paper we describe algebras and minimal generics of all subvarieties of $𝓑^{c}$, where 𝓑 is the variety of Boolean algebras.

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Addition and correction to the paper "Diagonal algebras"

38%

Płonka J.

Fundamenta Mathematicae

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1973

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tom 79

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nr 3

221-222

4

Exchange of independent sets in abstract algebras (III)

38%

Płonka J.

Colloquium Mathematicum

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1966

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tom 15

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nr 2

173-180

5

On functionally uniform symmetrical algebras

38%

Płonka J.

Colloquium Mathematicum

|

1966

|

tom 15

|

nr 2

181-188

6

T-independence in distributive lattices

32%

Płonka J., Poguntke W.

Colloquium Mathematicum

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1976

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tom 36

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nr 2

171-175

7

On distributive quad-lattices

26%

Płonka J.

Fundamenta Mathematicae

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1967

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tom 60

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nr 2

191-200

Ograniczanie wyników

4 Colloquium Mathematicum

2 Fundamenta Mathematicae

1 Discussiones Mathematicae - General Algebra and Applications

7 Płonka J.

1 Poguntke W.

1 2008

1 2001

1 1976

1 1973

1 1967

2 1966

The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras

Addition and correction to the paper "Diagonal algebras"

Exchange of independent sets in abstract algebras (III)

On functionally uniform symmetrical algebras

T-independence in distributive lattices

On distributive quad-lattices