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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0313-x,
author = {Igor Protasov},
title = {The combinatorial derivation and its inverse mapping},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {2176-2181},
zbl = {1300.20001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0313-x}
}
Igor Protasov. The combinatorial derivation and its inverse mapping. Open Mathematics, Tome 11 (2013) pp. 2176-2181. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0313-x/
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