On rings determined by zero products. (Q2847705)

A ring \(A\) is said to be zero product determined if for every biadditive map \(\varphi\) from \(A\times A\) into an arbitrary additive group \(S\) the following condition holds: if \(xy=0\) implies \(\varphi(x,y)=0\), then there exists an additive map \(f\colon A\to S\) such that \(\varphi(x,y)=f(xy)\) for all \(x,y\in A\). This concept was introduced in a slightly different context by the reviewer et al., [Linear Algebra Appl. 430, No. 5-6, 1486-1498 (2009; Zbl 1160.15018)], and has been after that studied in several papers by different authors.NEWLINENEWLINE In the paper under review, the author uses the ideas from these papers to obtain slight extensions of some of the results. In particular, he considers the question when are rings with idempotents, full matrix rings, and triangular rings zero product determined.