A Generalized Central Sets Theorem In Partial Semigroups
Abstract
The most powerful formulation of the Central Sets Theorem in an arbitrary semigroup was proved in the work of De, Hindman, and Strauss. The sets which satisfy the conclusion of the above Central Sets Theorem are called -sets. The original Central Sets Theorem was extended by J. McLeod for adequate commutative partial semigroups. In this work, we will extend the Central Sets Theorem obtained by taking all possible adequate sequences in a commutative adequate partial semigroup. We shall also discuss a sufficient condition for being a set -set in our context.
Cite
@article{arxiv.1809.01960,
title = {A Generalized Central Sets Theorem In Partial Semigroups},
author = {Arpita Ghosh},
journal= {arXiv preprint arXiv:1809.01960},
year = {2018}
}
Comments
10 pages. Final version. Accepted for publication in "Semigroup Forum". arXiv admin note: text overlap with arXiv:1309.7425, arXiv:1706.10010, arXiv:1302.4270, arXiv:1508.05280, arXiv:1711.06054, arXiv:1707.00787, arXiv:1703.05531 by other authors