We present a spectroscopic study with the derivation of the physical properties of 37 Balmer break galaxies, which have the necessary lines to locate them in star-forming-AGN diagnostic diagrams. These galaxies span a redshift range from 0.045 to 0.93 and are somewhat less massive than similar samples of previous works. The studied sample has multiwavelength photometric data coverage from the ultraviolet to MIR Spitzer bands. We investigate the connection between star formation and AGN activity via optical, mass-excitation (MEx) and MIR diagnostic diagrams. Through optical diagrams, 31 (84%) star-forming galaxies, 2 (5%) composite galaxies and 3 (8%) AGNs were classified, whereas from the MEx diagram only one galaxy was classified as AGN. A total of 19 galaxies have photometry available in all the IRAC/Spitzer bands. Of these, 3 AGN candidates were not classified as AGN in the optical diagrams, suggesting they are dusty/obscured AGNs, or that nuclear star formation has diluted their contributions. Furthermore, the relationship between SFR surface density (Sigma_{SFR}) and stellar mass surface density per time unit (Sigma_{M_{ast}/tau}) as a function of redshift was investigated using the [OII] lambda3727, 3729, Halpha lambda6563 luminosities, which revealed that both quantities are larger for higher redshift galaxies. We also studied the SFR and SSFR versus stellar mass and color relations, with the more massive galaxies having higher SFR values but lower SSFR values than less massive galaxies. These results are consistent with previous ones showing that, at a given mass, high-redshift galaxies have on average larger SFR and SSFR values than low-redshift galaxies. Finally, bluer galaxies have larger SSFR values than redder galaxies and for a given color the SSFR is larger for higher redshift galaxies.
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