Extension of $\mathcal {F}$-limits to general set families in the prime spectrum of a commutative ring

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2026年5月26日

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Oudika Ayoub,
Mouadi Hassan,
Driss Karim

摘要

We generalize the notion of the $\mathscr {F}$ $F$ -limit, initially introduced by Garcia–Ferreira and Ruza–Montilla, to any infinite index set I together with a family $\mathscr {F}_{\kappa }(I)$ $F_{κ} (I)$ of subsets of I that need not be an ultrafilter. This extension permits the definition of a topology on $\textrm{Spec}(R)$ $Spec (R)$ , called the $\mathscr {F}_{\kappa }(I)$ $F_{κ} (I)$ -limit topology, whose topological properties we study in detail.

Extension of \(\mathcal {F}\)-limits to general set families in the prime spectrum of a commutative ring

摘要