Publication details
A counter-example in the theory of E-solid completely 0-simple semigroups
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Semigroup Forum |
| MU Faculty or unit | |
| Citation | |
| web | https://doi.org/10.1007/s00233-025-10544-z |
| Doi | https://doi.org/10.1007/s00233-025-10544-z |
| Keywords | Regular E-solid semigroups; Completely 0-simple semigroups; Brandt semigroups; Rees matrix semigroups; Cores of completely simple semigroups; Varieties of completely simple semigroups; Varieties of nilpotent groups |
| Description | The purpose of this note is to document that the study of E-solid completely 0-simple semigroups cannot be reduced to the study of maximal completely simple subsemigroups of such semigroups. An example of a finite E-solid completely 0-simple semigroup S is provided such that S does not belong to the variety of semigroups generated by the collection of all maximal completely simple subsemigroups of S together with the five-element combinatorial Brandt semigroup B_2. This is in sharp contrast to the situation which is known to hold for arbitrary Brandt semigroups relatively to their maximal subgroups. |