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This book is aimed at presenting Algebraic Structure in Ternary Semigroups to the research scholars who are working in the field of algebra. A comprehensive coverage of topics required to the Ph.D scholars in various universities are discussed. This book is an out come of the vast results of authors. Mainly we introduced and studied about the concepts of irreducible, strongly irreducible, i -system of a ternary semigroup, primary, regular, completely regular of ternary semigroup and established some important consequences of the concepts. Also, we extended the concepts of Notherian, Archimedean, 2-Primal, annihilators, strongly regular, spectrums and super nilpotent of a ternary semigroup and established some interesting results relating to them.