PreprintCC0arXiv
Quotient structure of ultrafilters
Abstract
For ultrafilters u,v on N, the operation u/v is introduced and formalised which acts as quotient-like structures when v strongly divides u.Central to our study is the characterization of self-divisible ultrafilters in connection with the divisibility of u by u/v.Some results on the algebraic stability of multiplicative udempotents are presented.The paper also connects the combinatorial notions such as multiplicative delta sets,provoding characterization via self-divisible ultrafilters.
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BibTeX
@misc{singha2026quotient,
title = {{Quotient structure of ultrafilters}},
author = {Manoranjan Singha and Rohan Pradhan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.09010},
eprint = {2605.09010},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.09010},
note = {CC0},
}
RIS
TY - UNPB
TI - Quotient structure of ultrafilters
AU - Manoranjan Singha
AU - Rohan Pradhan
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2605.09010
UR - https://arxiv.org/abs/2605.09010
AB - For ultrafilters u,v on N, the operation u/v is introduced and formalised which acts as quotient-like structures when v strongly divides u.Central to our study is the characterization of self-divisible ultrafilters in connection with the divisibility of u by u/v.Some results on the algebraic stability of multiplicative udempotents are presented.The paper also connects the combinatorial notions such as multiplicative delta sets,provoding characterization via self-divisible ultrafilters.
ER -