which of the following algebraic structure is not a semi group
Answers
Step-by-step explanation:
non-empty set S, (S,*) is called a semigroup if it follows the following axiom: Closure:(a*b) belongs to S for all a,b ∈ S.
Answer:
If a*(b*c) = a*b*c for all a, b, and c belong to S or the elements adhere to the associative property under "*," an algebraic structure (P, *) is referred to as a semigroup.
Step-by-step explanation:
A set with a binary operation that has certain qualities that are similar to but less strict than those of a group is known as a "semigroup" in algebra. The set of positive integers with multiplication as the operation is an inspiring example of a semigroup. A semigroup is formally defined as a set S with a binary operation. A group of elements and processes that can be utilized to compute and resolve equations is known as an algebraic structure. The objects can be any mathematical thing you can conceive of, including numbers, polynomials, geometric shapes, points in space, and even card shuffles.
A monoid is a semigroup, but it also has an additional aspect of identity (E or e). If an algebraic structure (G, *) satisfies the following criteria, it is referred to as a monoid: Closure: If G is closed under operation *, all instances of a and b belong to the set G.
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