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A decision problem for varieties of commutative semigroups

Published online by Cambridge University Press:  17 April 2009

W.L. Cao
W.L. Cao
Affiliation:
Monash University Clayton, Victoria 3168, Australia
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For a first order formula P: ∀x1, …, ∀xn, ∃y1, …, ∃ym (u(x1, …, xn, y1, …, ym) ≡ v(x1, …, xn, y1, …, ym)) where u and v are two words on the alphabet {x1, …, xn, y1, …, ym}, and a finite set E of semigroup identities with xy ≡ yx in it, we prove that it is decidable whether P follows from E, that is whether all the semigroups in the variety defined by E satisfy P.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 3 , June 1993 , pp. 457 - 464
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Benninghofen, B., Kemmerich, S. and Richter, M. M., Systems of reductions (Springer-Verlag, Berlin, Heidelberg, New York, 1987).CrossRefGoogle Scholar