Aims. We present a spectroscopic study of the properties of 64 Balmer break galaxies that show signs of star formation. The studied sample of star-forming galaxies spans a redshift range from 0.094 to 1.475 with stellar masses in the range 10$^{8}-$10$^{12}$ $M_{odot}$. The sample also includes eight broad emission line galaxies with redshifts between 1.5 $<z<$ 3.0. Methods. We derived star formation rates (SFRs) from emission line luminosities and investigated the dependence of the SFR and specific SFR (SSFR) on the stellar mass and color. Furthermore, we investigated the evolution of these relations with the redshift. Results. We found that the SFR correlates with the stellar mass, our data is consistent with previous results from other authors in that there is a break in the correlation, which reveals the presence of massive galaxies with lower SFR values (i.e., decreasing star formation). We also note an anticorrelation for the SSFR with the stellar mass. Again in this case, our data is also consistent with a break in the correlation, revealing the presence of massive star-forming galaxies with lower SSFR values, thereby increasing the anticorrelation. These results might suggest a characteristic mass ($M_{0}$) at which the red sequence could mostly be assembled. In addition, at a given stellar mass, high-redshift galaxies have on average higher SFR and SSFR values than local galaxies. Finally, we explored whether a similar trend could be observed with redshift in the SSFR$-(u-B)$ color diagram, and we hypothesize that a possible $(u-B)_{0}$ break color may define a characteristic color for the formation of the red sequence.
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