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Abstract
In 1981, Tamura posed a number of problems regarding the axiomatic definition of inverse semigroups. The main goal of this article is to use automated reasoning to solve these problems. In the process, we find some new defining sets of identities for the class of inverse semigroups and provide a single identity for groups in terms of two binary operations.
ACKNOWLEDGMENT
We thank the referee for several useful suggestions regarding the form of the article and of [Citation1]. We also thank professors M. Branco, R. Padmanabhan, and B. M. Schein for their comments on a previous version of this article.
Partially supported by FCT and FEDER, Project ISFL-1-143 of Centro de Algebra da Universidade de Lisboa, and by FCT and PIDDAC through the project PTDC/MAT/69514/2006.
Notes
Communicated by V. Gould.