Rings close to Baer. (Q2461935)

A ring \(R\) is called a Baer ring if the left annihilator of each nonempty subset of \(R\) is a left ideal generated by an idempotent of \(R\). The class of Baer rings includes the domains, right (left) Noetherian right (left) PP rings and right (left) self-injective von Neumann regular rings. In this paper the author defines two kinds of homological dimensions, called \(\mathcal A\)-injective dimension and \(\mathcal A\)-flat dimension, which measure how far away a ring is from being a Baer ring. The author shows that these dimensions have nice properties when the ring in question is an AC ring, where \(R\) is called a left AC ring if the left annihilator of each nonempty subset of \(R\) is a cyclic left ideal.