Let be a commutative ring with identity. The small finitistic dimension of is defined to be the supremum of projective dimensions of -modules with finite projective resolutions. In this paper, we characterize a ring with using finitely generated semiregular ideals, tilting modules, cotilting modules of cofinite type and vaguely associated prime ideals. As an application, we obtain that if is a Noetherian ring, then where is the grade of on . We also show that a ring satisfies if and only if is a ring. As applications, we show that the small finitistic dimensions of strong Prüfer rings and s are at most one. Moreover, for any given , we obtain a total ring of quotients satisfying .
"THE SMALL FINITISTIC DIMENSIONS OF COMMUTATIVE RINGS." J. Commut. Algebra 15 (1) 131 - 138, Spring 2023. https://doi.org/10.1216/jca.2023.15.131