  In 1969, Osofsky proved that a chained ring (i.e., local arithmetical ring)
with zero divisors has infinite weak global dimension; that is, the weak global
dimension of an arithmetical ring is 0, 1, or infinite. In 2007, Bazzoni and
Glaz studied the homological aspects of Prufer-like rings, with a focus on
Gaussian rings. They proved that Osofsky's aforementioned result is valid in
the context of coherent Gaussian rings (and, more generally, in coherent Prufer
rings). They closed their paper with a conjecture sustaining that ``the weak
global dimension of a Gaussian ring is 0, 1, or infinite. In 2010,
Bakkari-Kabbaj-Mahdou provided an example of a Gaussian ring which is neither
arithmetical nor coherent and has an infinite weak global dimension. In 2011,
Abuhlail-Jarrar-Kabbaj introduced and investigated the new class of fqp-rings
which stands strictly between the two classes of arithmetical rings and
Gaussian rings. Then, they proved the Bazzoni-Glaz conjecture for fqp-rings.
This paper surveys a few recent works in the literature on the weak global
dimension of Prufer-like rings making this topic accessible and appealing to a
broad audience. As a prelude to this, the first section of this paper provides
full details for Osofsky's proof of the existence of a module with infinite
projective dimension on a chained ring. Numerous examples -arising as trivial
ring extensions- are provided to illustrate the concepts and results involved
in this paper.
