Varieties without minimal generators. (Q5932593)

We recall that by {minimal varietal generator} for a variety we mean a regular projective finitely presentable regular generator such that none of its retracts is a regular generator, and even a unique one. While many familiar varieties have a minimal varietal generator, in this paper the authors present a variety having no minimal varietal generator at all and a variety having two non-isomorphic minimal varietal generators. Moreover, they demonstrate that the same effects can happen with respect to a weaker notion of minimality and are common even in module categories.