For the first time, the sulphur abundance relative to hydrogen (S/H) in the Narrow Line Regions of a sample of Seyfert 2 nuclei (Sy 2s) has been derived via direct estimation of the electron temperature. Narrow emission line intensities from the SDSS DR17 [in the wavelength range 3000 < 𝜆(Å) < 9100] and from the literature for a sample of 45 nearby (𝑧 < 0.08) Sy 2s were considered. Our direct estimates indicate that Sy 2s have similar temperatures in the gas region where most of the S + ions are located in comparison with that of star-forming regions (SFs). However, Sy 2s present higher temperature values (∼ 10 000 K) in the region where most of the S 2+ ions are located relative to that of SFs. We derive the total sulphur abundance in the range of 6.2 < ∼ 12 + log(S/H) < ∼ 7.5, corresponding to 0.1 -1.8 times the solar value. These sulphur abundance values are lower by ∼ 0.4 dex than those derived in SFs with similar metallicity, indicating a distinct chemical enrichment of the ISM for these object classes. The S/O values for our Sy 2 sample present an abrupt (∼ 0.5 dex) decrease with increasing O/H for the high metallicity regime [12 + log(O/H) > ∼ 8.7)], what is not seen for the SFs. However, when our Sy 2 estimates are combined with those from a large sample of star-forming regions, we did not find any dependence between S/O and O/H.

We present oxygen abundances relative to hydrogen (O/H) in the narrow line regions (NLRs) gas phases of Seyferts 1 (Sy 1s) and Seyferts 2 (Sy 2s) Active Galactic Nuclei (AGNs). We used fluxes of the optical narrow emission line intensities [3 500 < 𝜆(Å) < 7 000] of 561 Seyfert nuclei in the local universe (𝑧 0.31) from the second catalog and data release (DR2) of the BAT AGN Spectroscopic Survey, which focuses on the Swift-BAT hard X-ray ( 10 keV) detected AGNs. We derived O/H from relative intensities of the emission lines via the strong-line methods. We find that the AGN O/H abundances are related to their hosts stellar masses and that they follow a downward redshift evolution. The derived O/H together with the hard X-ray luminosity (𝐿 X ) were used to study the X-ray luminosity-metallicity (𝐿 X -𝑍 NLR ) relation for the first time in Seyfert galaxies. In contrast to the broad-line focused (𝐿 X -𝑍 BLR ) studies, we find that the 𝐿 X -𝑍 NLR exhibit significant anti-correlations with the Eddington ratio (𝜆 Edd ) and these correlations vary with redshifts. This result indicates that the low-luminous AGNs are more actively undergoing Interstellar Medium (ISM) enrichment through star formation in comparison with the more luminous X-ray sources. Our results suggest that the AGN is somehow driving the galaxy chemical enrichment, as a result of the inflow of pristine gas that is diluting the metal rich gas, together with a recent cessation on the circumnuclear star-formation.