Let $T$ be a dense subsemigroup of $((0,\infty),+)$ and put $S = T \cap (0,1)$. In this paper we show that $(S,\dot{+})$ is a commutative adequate partial semigroup, where $x \dot{+} y = x+y$ whenever $x+y \in S$. First, we prove that the semigroup of ultrafilters near zero of $S$ is an adequacy kernel of $S$; consequently, every result that holds for commutative adequate partial semigroups also holds for the semigroup of ultrafilters near zero. Second, we demonstrate that $(S,\dot{+})$ does not satisfy the $(SFC)$ condition for commutative adequate partial semigroups. Finally, we propose a Følner density equipped with a suitable operation on $S$, which aids the study of density near zero.
Akbari Tootkaboni, M., Bagheri Salec, A., & Abbas, S. (2025). The semigroup of ultrafilters near zero as adequacy kernel of a partial semigroup. Measure Algebras and Applications, 3(2), -. doi: 10.22091/maa.2026.15177.1052
MLA
Mohammad Akbari Tootkaboni; Alireza Bagheri Salec; Suad Abbas. "The semigroup of ultrafilters near zero as adequacy kernel of a partial semigroup". Measure Algebras and Applications, 3, 2, 2025, -. doi: 10.22091/maa.2026.15177.1052
HARVARD
Akbari Tootkaboni, M., Bagheri Salec, A., Abbas, S. (2025). 'The semigroup of ultrafilters near zero as adequacy kernel of a partial semigroup', Measure Algebras and Applications, 3(2), pp. -. doi: 10.22091/maa.2026.15177.1052
VANCOUVER
Akbari Tootkaboni, M., Bagheri Salec, A., Abbas, S. The semigroup of ultrafilters near zero as adequacy kernel of a partial semigroup. Measure Algebras and Applications, 2025; 3(2): -. doi: 10.22091/maa.2026.15177.1052
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