Question

An algebraic structure ____ is called a semigroup.​

Answer 1

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An algebraic structure______is called a semigroup.

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Brother/Sister your correct answer will be:-

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.

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Answer 2

Answer:

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

Step-by-step explanation:

Step 1: Associative binary operation: Let G be a non-empty set. Then a binary operation * is called associative if $\forall a, b, c \in G$ such that a *(b * c)=(a * b) * c.

Step 2: 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.

Step 3: A semigroup is an algebraic structure made up of an associative binary operation and a non-empty set. Early in the 20th century, semigroups were first formally studied.

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