Question

The algebraic system (A:*) is called a group if​

Answer 1

Answer:

Explanation: A non empty set A is called an algebraic structure w.r.t binary operation “*” if (a*b) belongs to S for all (a*b) belongs to S. ... Explanation: A monoid(B,*) is called Group if to each element there exists an element c such that (a*c)=(c*a)=e.

Answer 2

An algebraic system (A, *) is said to be a group if the following conditions are met:

• Closed operation: When the results of a mathematical operation are always defined, this is referred to as closure.
• Associative operation: A calculation that gives the same answer regardless of how the numbers are grouped is known as an associative operation.
• There is an identity in A.
• In A, every element has an inverse.

A monoid, semigroup, or algebraic structure is always a group.