Minimal generators in varieties (Q1840753)

A variety \(V\) of universal algebras can have several equational presentations. Resulting free algebras over a one-element set can be characterized as finitely presentable regular projective regular generators in \(V\). The paper discusses the existence of a minimal generator of this kind. Investigations were continued in a subsequent paper of the author and the reviewer [\textit{H.-E. Porst} and \textit{J. Rosický}, ``Varieties without minimal generators'', Algebra Univers. 45, No. 1, 23-33 (2001; Zbl 1044.18001)].