A binary operation * over real numbers is said to be associative if (x * y) * z = x * (y * z) and it is said to be reducible if x * y = x * z or y * w = z * w if and ...

This is a preview. Log in through your library . Journal Information The Mathematical Gazette is the original journal of the Mathematical Association and it is now over a century old. Its readership ...

Semigroups, algebraic structures defined by a set equipped with an associative binary operation, are a cornerstone within modern algebra. Their study encompasses both abstract theoretical development ...