Wyniki wyszukiwania

1

Subdirect decompositions of algebras from 2-clone extensions of varieties

100%

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.

2

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On the number of independent elements in finite abstract algebras with two binary symmetrical operations

50%

Płonka J.

Colloquium Mathematicum

|

1968

|

tom 19

|

nr 1

9-21

3

On the join of equational classes of idempotent algebras and algebras with constants

50%

Płonka J.

Colloquium Mathematicum

|

1973

|

tom 27

|

nr 2

193-195

4

On connections between the decomposition of an algebra into sums of direct systems of subalgebras

50%

Płonka J.

Fundamenta Mathematicae

|

1974

|

tom 84

|

nr 3

237-244

5

On the number of polynomials of a universal algebra, I

45%

Grätzer G., Płonka J., Sekanina A.

Colloquium Mathematicum

|

1970-1971

|

tom 22

|

nr 1

9-11

6

On the number of independent elements in finite abstract algebras having a binary operation

44%

Płonka J.

Colloquium Mathematicum

|

1966

|

tom 14

|

nr 1

189-201

7

On automorphism groups of relational systems and universal algebras

44%

Płonka J.

Colloquium Mathematicum

|

1979

|

tom 42

|

nr 1

341-344

8

On equational classes of abstract algebras defined by regular equations

44%

Płonka J.

Fundamenta Mathematicae

|

1969

|

tom 64

|

nr 2

241-247

9

On bounding congruences in some algebras having the lattice structure

44%

Płonka J.

Banach Center Publications

|

1982

|

tom 9

|

nr 1

203-207

10

On the number of polynomials of a universal algebra, II

38%

Grätzer G., Płonka J.

Colloquium Mathematicum

|

1970-1971

|

tom 22

|

nr 1

13-19

11

On bases with respect to a closure operator with the exchange property

38%

Płonka J.

Colloquium Mathematicum

|

1963

|

tom 10

|

nr 1

25-29

12

On groups in which idempotent reducts form a chain

38%

Płonka J.

Colloquium Mathematicum

|

1974

|

tom 29

|

nr 1

87-91

13

On the number of polynomials of a universal algebra, III

38%

Płonka J.

Colloquium Mathematicum

|

1970-1971

|

tom 22

|

nr 2

177-180

14

On the arity of idempotent reduct of abelian groups

38%

Płonka J.

Colloquium Mathematicum

|

1973

|

tom 27

|

nr 2

175-176

15

Remarks on diagonal and generalized diagonal algebras

38%

Płonka J.

Colloquium Mathematicum

|

1966

|

tom 15

|

nr 1

19-23

16

Associative and idempotent algebras are at most ternary

38%

Płonka J.

Colloquium Mathematicum

|

1976

|

tom 36

|

nr 2

177-180

17

On the number of polynomials of a universal algebra, IV

38%

Płonka J.

Colloquium Mathematicum

|

1972

|

tom 25

|

nr 1

11-14

18

Homogeneous algebras are simple

32%

Ganter B., Płonka J., Werner H.

Fundamenta Mathematicae

|

1973

|

tom 79

|

nr 3

217-220

19

A characterization of semilattices

32%

Grätzer G., Płonka J.

Colloquium Mathematicum

|

1970-1971

|

tom 22

|

nr 1

21-24

20

On some partitions of a graph, I

32%

Majcher Z., Płonka J.

Applicationes Mathematicae

|

1987

|

tom 19

|

nr 3-4

519-529

Ograniczanie wyników

Subdirect decompositions of algebras from 2-clone extensions of varieties

On the number of independent elements in finite abstract algebras with two binary symmetrical operations

On the join of equational classes of idempotent algebras and algebras with constants

On connections between the decomposition of an algebra into sums of direct systems of subalgebras

On the number of polynomials of a universal algebra, I

On the number of independent elements in finite abstract algebras having a binary operation

On automorphism groups of relational systems and universal algebras

On equational classes of abstract algebras defined by regular equations

On bounding congruences in some algebras having the lattice structure

On the number of polynomials of a universal algebra, II

On bases with respect to a closure operator with the exchange property

On groups in which idempotent reducts form a chain

On the number of polynomials of a universal algebra, III

On the arity of idempotent reduct of abelian groups

Remarks on diagonal and generalized diagonal algebras

Associative and idempotent algebras are at most ternary

On the number of polynomials of a universal algebra, IV

Homogeneous algebras are simple

A characterization of semilattices

On some partitions of a graph, I