ASTE observations in the 345 GHz window towards the HII region N113 of the Large Magellanic Cloud

N113 is an HII region located in the central part of the Large Magellanic Cloud (LMC) with an associated molecular cloud very rich in molecular species. Most of the previously observed molecular lines cover the frequency range 85-270 GHz. Thus, a survey and study of lines at the 345 GHz window is required in order to have a more complete understanding of the chemistry and excitation conditions of the region. We mapped a region of 2.5' x 2.5' centered at N113 using the Atacama Submillimeter Telescope Experiment in the 13CO J=3-2 line with an angular and spectral resolution of 22" and 0.11 km/s, respectively. In addition, we observed 16 molecular lines as single pointings towards its center. For the molecular cloud associated with N113, from the 13CO J=3-2 map we estimate LTE and virial masses of about 1x10^4 and 4.5x10^4 M_sun, respectively. Additionally, from the dust continuum emission at 500 micron we obtain a mass of gas of 7x10^3 M_sun. Towards the cloud center we detected emission from: 12CO, 13CO, C18O (3-2), HCN, HNC, HCO+, C2H (4-3), and CS (7-6); being the first reported detection of HCN, HNC, and C2H (4-3) lines from this region. The CS (7-6) which was previously tentatively detected is confirmed in this study. By analyzing the HCN, HNC, and C2H, we suggest that their emission may arise from a photodissociation region (PDR). Moreover, we suggest that the chemistry involving the C2H in N113 can be similar to that in Galactic PDRs. Using the HCN J=4-3, J=3-2, and J=1-0 lines in a RADEX analysis we conclude that we are observing very high density gas, between some 10^5 and 10^7 cm-3.