Publication details
Reducibility vs. definability for pseudovarieties of semigroups
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Algebra and Computation |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1142/S0218196716500648 |
| Field | General mathematics |
| Keywords | Pseudovariety; relatively free profinite semigroup; ordered semigroup; completely regular semigroup; commutative semigroup; group |
| Description | It is easy to show that a pseudovariety which is reducible with respect to an implicit signature sigma for the equation x=y can also be defined by sigma-identities. We present several negative examples for the converse using signatures in which the pseudovarieties are usually defined. An ordered example issue from the extended Straubing–Thérien hierarchy of regular languages is also shown to provide a positive example. |
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