On identities in groups of fractions of cancellative semigroups
نویسندگان
چکیده
منابع مشابه
On Identities in Groups of Fractions of Cancellative Semigroups
To solve two problems of Bergman stated in 1981, we construct a group G such that G contains a free noncyclic subgroup (hence, G satisfies no group identity) and G, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.
متن کاملCrossability of cancellative Kleene semigroups
Every cancellative Kleene semigroup satisfies Eilenberg's theorem. Résumé. — Si S est un semigroupe simplifiable de type Kleene, alors S satisfait le théorème d'Eilenberg.
متن کاملSubsemigroups of Cancellative Amenable Semigroups
We generalize a theorem of Frey by giving sufficient conditions for a subsemigroup T of a cancellative left amenable semigroup S to be left amenable. In particular, we show that if S is left amenable and T does not contain a free subsemigroup on two generators, then T is left amenable as well.
متن کاملAutomatic Presentations for Cancellative Semigroups
This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-05-07903-7