Gruppo , semigruppo, monoide .Lez 3/5

Group, semigroup, monoid: the main algebraic structures. In previous lessons, the following concepts were explained: Law of internal composition Commutative, associative, and distributive properties. Neutral element Simplifiable element Symmetric element which are preparatory to this lesson. Having defined an algebraic structure, we will introduce the concepts of semigroup and group, which are the two algebraic structures in which a single law of internal composition is defined (called the star law in our case). We will see the cases in which the semigroup or group is Abelian (or commutative) and the case in which a semigroup is a monoid. We will also list the properties of groups. Examples will better clarify these seemingly theoretical and very abstract concepts. #group #semigroup #monoid -