Question

An algebraic structure ____ is called a semigroup.​

Answer 1

An algebraic structure  (P,*)   is called a semigroup.

Explanation:

       An algebraic structure (P,*) is called a semigroup if a*(b*c) = (a*b)*c for all a,b,c belongs to S or the elements follow associative property under “*”. (Matrix,*) and (Set of integers,+) are examples of semigroup.

Answer 2

Answer:

An algebraic structure in which binary operation is associative is called semi group.

Step-by-step explanation:

Associative binary operation: Let $G$ be a non-empty set. Then a binary operation * is called associative if ∀ $a,b,c$ ∈ $G$ such that

$a*(b*c)=(a*b)*c$.

Algebraic structure: A non-empty set equipped with one or more binary operations is called algebraic structure.

Therefore, an algebraic structure in which binary operation is associative is called semi group.

For example: $(N,+)$, $(Z,+)$ are examples of semigroup.

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