Tanushree Biswas, Dibyendu De, and Ram Krishna Paul
Matrices centrally image partition regular near 0
||July 20, 2015
||Central sets near 0, algebra in the Stone-Čech compactification, image partition regularity of matrices.
||Primary 05D10, Secondary 22A15, 54H13
Hindman and Leader first investigated Ramsey theoretic
properties near 0 for dense subsemigroups of (R, +). Following them,
the notion of image partition regularity near zero for matrices was introduced by De and Hindman. It was also shown there that like image
partition regularity over N, the main source of infinite image partition
regular matrices near zero are Milliken-Taylor matrices.
But except for constant multiples of the Finite Sum matrix,
no other Milliken-Taylor matrices have images in central sets.
In this regard the notion of centrally image partition
regular matrices were introduced. In the present paper we propose the notion
of matrices that are centrally image partition regular matrices
near zero for dense subsemigroups
of (R, +) and show that for infinite matrices these may be different from
centrally image partition regular matrices,
unlike the situation for finite matrices.
Department of Mathematics, University of Kalyani, Kalyani-741235, West Bengal, India
Department of Mathematics, University of Kalyani, Kalyani-741235,
West Bengal, India
Ram Krishna Paul:
Department of Mathematics, Nagaland University, Lumami-798627, Nagaland, India