Bases of lines provide useful presentations of finite height modular lattices, acyclic ones being related to amenable properties in equational and representation theory. It is shown that some (equivalently: any) base of L is acyclic if and only if L has exactly 2d(L)−s(L) join irreducibles; moreover, that this is the minimal possible number for any L. Here d(L) denotes the height and s(L) the number of maximal congruences of L.
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