Department of Mathematics
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John Baez (see [1]) defines the concept of a unital shelf as an algebraic system (A; *, e) admitting a two-sided unit and satisfying the left self-distributive law x * (y * z) = (x * y) * (x * z). Left distributive systems occur in several areas of mathematics: symmetric spaces, the homology theory of algebraic structures, group conjugates, quandles etc (e.g. [2]). Here we describe three kinds of integer sequences associated with the variety of all unital shelves: (i) the free spectrum, (ii) the pn-sequence and (iii) the Tarski spectrum. In particular, we solve the word problem for the equational theory of unital shelves.

I thank Dr. Craig Platt for bringing my attention to this topic when we met outside the Machray Hall during a false fire-alarm break on June 25th, 2015.

1. John Baez diary for June, 2015
2. Victoria Lebed, Cohomology of finite monogenic self-distributive structures pdf