Weak alg-universality and Q-universality of semigroup quasivarieties

نویسندگان

  • M. Demlová
  • V. Koubek
چکیده

In an earlier paper, the authors showed that standard semigroups M1, M2 andM3 play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by M2 and M3 are neither relatively alg-universal nor Q-universal, while there do exist finite semigroups S2 and S3 generating the same semigroup variety as M2 and M3 respectively and the quasivarieties generated by S2 and/or S3 are quasivar-relatively ff -alg-universal and Quniversal (meaning that their respective lattices of subquasivarieties are quite rich). An analogous result on Q-universality of the variety generated byM2 was obtained by M.V. Sapir; the size of our semigroup is substantially smaller than that of Sapir’s semigroup.

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تاریخ انتشار 2010