On The Minors Defined By A Generic Matrix

In this paper, the second syzygies of minors defined by a generic matrix are studied for certain sizes of minors. The syzygies are explicitly given and are constructed by utilizing the division algorithm and the associated standard bases (also known as Gröbner bases) theory on the polynomial ring over integers that the author studied in a separate paper, cf. Ma (1994) stemed from Buchbergerʹsceleberated pioneering work on the theory, c.f., Buchberger (1985), a good source for such study