The semiring of topologizing filters of a ring (Q1101817)

Let R be a ring and \(\Lambda\) (R) the lattice of right ideals of R. A meet-preserving closure operator on \(\Lambda\) (R) is called a nucleus and the concept of pre-nucleus is obtained by dropping the requirement of idempotency in this definition. A pre-nucleus is respectful when it preserves quotients by elements of R. \textit{K. L. Chew} [Bull. Math. Soc. Nanyang Univ. 1965, 1-20 (1965; Zbl 0152.017)] proved that there exists a natural bijection between Gabriel filters on \(\Lambda\) (R) and respectful nuclei (modular closure operators) on \(\Lambda\) (R). In the paper under review, the author extends this correspondence to a bijection between topologizing filters and respectful pre-nuclei on \(\Lambda\) (R).