15 авг. 2015 г. · A subgroup is a subset of a group that is itself closed under the group operation. A semigroup is a set equipped with an operation that is merely associative.

23 янв. 2012 г. · Group theory is a subtheory of the theory of semigroups, so groups can only end more important than semigroups if a subtheory S of a theory T ...

29 февр. 2016 г. · A nonempty semigroup is a group if and only if every element is a weak inverse of exactly one element.

30 окт. 2011 г. · Let G be the free group generated by the elements of X modulo the normal subgroup generated by the relations given by the multiplication table in X.

3 янв. 2022 г. · Let T be a semigroup ("time") and X a set ("state space") corresponding to a dynamical system (in particular T acts on X in a known way, (t,x)↦t ...

4 окт. 2019 г. · A semigroup is a set S together with a binary operation ∗ that is, a function ∗:S×S→S that satisfies the associative property.

24 сент. 2019 г. · In general algebraic structures, the kernel of a homomorphism f:X→Y is defined just as for semigroups: kerf:={(x,x′):f(x)=f(x′)}.

19 мая 2012 г. · The difference is that an element of a monoid doesn't have to have inverse, while an element of a group does. For example, N is a monoid under ...

28 сент. 2015 г. · Is every semigroup with weak division a group? If not, is it true for commutative semigroups? Edit: I've just become aware of this question, ...

26 июл. 2020 г. · The answer is no: associative quasigroups are always inverse semigroups, but inverse semigroups are not necessarily associative quasigroups.