Existence of dualizing complexes (Q1076081)

Let A be a commutative Noetherian ring (with identity). In J. Algebra 44, 246-261 (1977; Zbl 0345.13011)], the reviewer introduced the concept of acceptable ring, and in Math. Proc. Camb. Philos. Soc. 82, 197-213 (1977; Zbl 0363.13008)], he showed that if A is possesses a dualizing complex then it is acceptable. It is also known that if A possesses a dualizing complex, then A has a canonical module. The interesting paper under review is concerned, among other things, with converse statements to the above. One of its main results is that if A satisfies the condition (S\({}_ 2\)), is finite-dimensional and acceptable and has a canonical module, then A possesses a dualizing complex. Examples are given to demonstrate the importance of the hypothesis that A is acceptable and the hypothesis that A has a canonical module. Another striking result from the paper is that, in the case when A is local, A has a dualizing complex if and only if A is acceptable and every homomorphic image of A has a canonical module.