Department of Mathematics
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Algebras can be characterized in various ways: by means of identities, implications, by giving the list of all subdirectly irreducible members, by constructing the free algebra etc. Here we use the concept of "term spectrum" to describe certain varieties of algebras. The term spectrum of an algebra A is the integer sequence p(n) of essentially n- ary terms of A. In this presentation, we characterize several varieties of algebras by their term spectra. In particular, we show the minimal extension property of the initial segments of some representable sequences including a non-trivial sequence associated with elliptic cubics.

References

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