Non-finitely based finite involution semigroups with finitely based semigroup reducts
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Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.
Abstract
Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.
참고문헌 (10)
- S. Burris, "A Course in Universal Algebra" (1981), Springer Verlag
- M. Jackson, "Small Semigroup Related Structures with Infinite Properties", Ph.D., pp.1999
- M. Jackson, "Finitely based, finite sets of words", Internat. J. Algebra Comput, 10, pp.683~708 (2000)
- M. Jackson, "Fields of Logic and Computation", pp.414~443 (2010), Springer
- E. W. H. Lee, "A class of finite semigroups without irredundant bases of identities", Yokohama Math. J, 61, pp.1~28 (2015)
- E. W. H. Lee, "Finitely based nite involution semigroups with non-infitely based reducts", Quaest. Math, 39, pp.217~243 (2016)
- E. W. H. Lee, "Varieties of involution monoids with extreme properties", Q. J. Math.
- P. Perkins, "Bases for equational theories of semigroups", J. Algebra, 11, pp.298~314 (1969)
- G. Pollak, "On almost simple semigroup identitie", Colloq. Math. Soc. Janos Bolyai, 39, pp.287~323 (1985), North-Holland
- M. V. Volkov, "The finite basis problem for finite semigroups", Sci. Math. Jpn, 53, pp.171~199 (2001)