algebra universalis

, Volume 38, Issue 4, pp 422–449 | Cite as

The probability of triviality

  • J. Berman
  • H. Lakser


Given a variety \( \cal V \) of algebras, what is the probability that for an arbitrary identity p \( \approx \) q the only algebra in \( \cal V \) that satisfies p \( \approx \) q is the trivial algebra? More generally, if \( \cal W \) is a subvariety of \( \cal V \) what is the probability that p \( \approx \) q together with the identities of \( \cal V \) forms an equational basis for \( \cal W \)? We consider these questions for various \( \cal V \) and \( \cal W \) and we provide criteria that allow for explicit determination of these probabilities.

Key words and phrases: Variety, identity, probability, Fraser-Horn Property. 


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Copyright information

© Birkhäuser Verlag Basel, 1997

Authors and Affiliations

  • J. Berman
    • 1
  • H. Lakser
    • 2
  1. 1.Department of Mathematics, Statistics and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607-7045, USA. E-mail: jberman@uic.eduUS
  2. 2.Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada. E-mail: hlakser@cc.umanitoba.caCA

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