Weak alg-universality and Q-universality of semigroup quasivarieties
نویسندگان
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.
منابع مشابه
On Universality of Semigroup Varieties
To Professor Jǐŕı Rosický on his 60th birthday Abstra t. A category K is called α-determined if every set of non-isomorphic Kobjects such that their endomorphism monoids are isomorphic has a cardinality less than α. A quasivariety Q is called Q-universal if the lattice of all subquasivarieties of any quasivariety of finite type is a homomorphic image of a sublattice of the lattice of all subqua...
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