The element abundances of galaxies provide crucial insights into their formation and evolution. Using high-resolution integral field unit data from the Mapping Nearby Galaxies at Apache Point Observatory survey, we analyze the central spectra (0–0.5 R _e ) of 1185 quenched galaxies ( z = 0.012−0.15) to study their element abundances and stellar populations. We employ the full-spectrum fitting code alf to derive stellar ages and element abundances from synthetic spectra and empirical libraries. Our key findings are: (1) the central velocity dispersion ( σ _* ) is the most effective parameter correlating with the (relative) element abundances, especially [Na/Fe], [Mg/Fe], [C/Fe], and [N/Fe], outperforming M _* and M _* / R _e ; (2) when binned by σ _* , the relative abundances of Na, Mg, C, and N remain stable across different formation times ( T _form ), suggesting these elements are primarily influenced by the burstiness of star formation (traced by σ _* ) rather than prolonged evolutionary processes; and (3) Fe and Ca show little variation with σ _* , indicating weaker sensitivity to σ _* -driven processes. However, T _form has a global influence on all elements, contributing to their overall chemical evolution, although this is secondary to σ _* for most elements. These results support the primary role of σ _* in shaping the abundance patterns, likely stemming from the connection with central massive black holes and possibly also that with dark matter halos, which influences the burstiness of star formation histories.