Abstract
Column-row products have zero determinant over any commutative ring. In this paper we discuss the converse. For domains, we show that this yields a characterization of pre-Schreier rings, and for rings with zero divisors we show that reduced pre-Schreier rings have this property.Finally, for the rings of integers modulo n, we determine the 2x2 matrices which are (or not) full and their numbers.
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