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The combinatorial derivation and its inverse mapping

100%

Protasov I.

Open Mathematics

2013

tom 11

nr 12

2176-2181

Let G be a group and P G be the Boolean algebra of all subsets of G. A mapping Δ: P G → P G defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: P X→ P X, A ↦ A d, where X is a topological space and A d is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in P G such that Δ(A) ∈ I and ∇(A) ⊆ I for each A ∈ I then I = P G.

On some congruences of power algebras

81%

Pilitowska A., Zamojska-Dzienio A.

Open Mathematics

2012

tom 10

nr 3

987-1003

In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class of non-trivial subvarieties of the variety of all semilattice ordered modes (modals).

Ograniczanie wyników

2 Open Mathematics

1 Pilitowska A.

1 Protasov I.

1 Zamojska-Dzienio A.

1 2013

1 2012

Wyniki wyszukiwania

The combinatorial derivation and its inverse mapping

On some congruences of power algebras