A Semigroup Is Finite Iff It Is Chain-Finite and Antichain-Finite
A Semigroup Is Finite Iff It Is Chain-Finite and Antichain-Finite
A subset A of a semigroup S is called a chain (antichain) if ab∈{a,b} (ab∉{a,b}) for any (distinct) elements a,b∈A. A semigroup S is called periodic if for every element x∈S there exists n∈N such that xn is an idempotent. A semigroup S is called (anti)chain-finite if S contains no …