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Affine Parts of Algebraic Theories II

Published online by Cambridge University Press:  20 November 2018

J. R. Isbell ,
M. I. Klun  and
S. H. Schanuel
J. R. Isbell
Affiliation:
State University of New York at Buffalo, Amherst, New York
M. I. Klun
Affiliation:
State University of New York at Buffalo, Amherst, New York
S. H. Schanuel
Affiliation:
State University of New York at Buffalo, Amherst, New York
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 231 - 237
Copyright
Copyright © Canadian Mathematical Society 1978

References

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