Geodesic
Affine Parts of Algebraic Theories II
Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 231-237

Voir la notice de l'article provenant de la source Cambridge University Press

This paper concerns relative complexity of an algebraic theory T and its affine part A, primarily for theories TR of modules over a ring R. TR, AR and R itself are all, or none, finitely generated or finitely related. The minimum number of relations is the same for TR and AR. The minimum number of generators is a very crude invariant for these theories, being 1 for AR if it is finite, and 2 for TR if it is finite (and 1 ≠ 0 in R). The minimum arity of generators is barely less crude: 2 for TR} and 2 or 3 for AR (1 ≠ 0). AR is generated by binary operations if and only if R admits no homomorphism onto Z2. 
Isbell, J. R.; Klun, M. I.; Schanuel, S. H. Affine Parts of Algebraic Theories II. Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 231-237. doi: 10.4153/CJM-1978-021-3
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[1] 1. Isbell, J. R., Klun, M. I., and Schanuel, S. H., Affine parts of algebraic theories I, Journal of Algebra U (1977), 1–8. Google Scholar

[2] 2. Tarski, A., Equational logic and equational theories of algebras, Contributions to Math. Logic Colloquium, Hanover, (1966), 275–288 (Amsterdam, 1968). Google Scholar

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