International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 830718, 7 pages
http://dx.doi.org/10.1155/2012/830718
Research Article

Combined Algebraic Properties of IP* and Central* Sets Near 0

Dibyendu De1 and Ram Krishna Paul2

1Department of Mathematics, University of Kalyani, West Bengal, Kalyani 741235, India
2Department of Mathematics, National Institute of Technology, South Sikkim, Ravangla 737139, India

Received 25 March 2012; Accepted 26 June 2012

Academic Editor: Manfred Moller

Copyright © 2012 Dibyendu De and Ram Krishna Paul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is known that for an IP* set 𝐴 in ℕ and a sequence ⟨ 𝑥 𝑛 ⟩ ∞ 𝑛 = 1 there exists a sum subsystem ⟨ 𝑦 𝑛 ⟩ ∞ 𝑛 = 1 of ⟨ 𝑥 𝑛 ⟩ ∞ 𝑛 = 1 such that 𝐹 𝑆 ( ⟨ 𝑦 𝑛 ⟩ ∞ 𝑛 = 1 ) ∪ 𝐹 𝑃 ( ⟨ 𝑦 𝑛 ⟩ ∞ 𝑛 = 1 ) ⊆ 𝐴 . Similar types of results also have been proved for central* sets. In this present work we will extend the results for dense subsemigroups of ( ( 0 , ∞ ) , + ) .