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In this paper we study some interesting properties of regular ternary semigroups, completely regular ternary semigroups, intra-regular ternary semigroups and characterize them by using various ideals of ternary semigroups.
In the paper, the following concept are defined: (i) a minimal left (right, two-sided) ideal with respect to a subset of a semigroup , (ii) a kernel with respect to a subset of a semigroup , and their basic properties are investigated.
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