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An algebraic structure _________ is called a semigroup.ans.

Question

An algebraic structure _________ is called a semigroup.ans.

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Solution

An algebraic structure is called a semigroup if it satisfies the following two conditions:

  1. Closure: The operation is closed. This means that if you take any two elements in the set and perform the operation, the result will still be in the set.

  2. Associativity: The operation is associative. This means that for any three elements a, b, and c in the set, the equation (a * b) * c = a * (b * c) holds true.

Here, "*" represents the binary operation of the semigroup.

Please note that a semigroup does not require the existence of an identity element or the existence of inverse elements, which distinguishes it from other algebraic structures like groups.

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Condition of semigroup homomorphism should be ____________ans.f(x) * f(y) = f(y)f(x * x) = f(x * y)f(x * y) = f(x) * f(y)f(x) = f(y) Previous Marked for Review Next

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