On the almost Gorenstein property of determinantal rings.

In this paper, we investigate the question of when the determinantal ring <italic>R</italic> over a field <italic>k</italic> is an almost Gorenstein local/graded ring in the sense of [<xref>14</xref>]. As a consequence of the main result, we see that if <italic>R</italic> is a non-Gorenstein almost Gorenstein local/graded ring, then the ring <italic>R</italic> has a minimal multiplicity. [ABSTRACT FROM AUTHOR]