The Minimality and Maximality of n-ideals in n-ary Semigroups (European Journal of Pure and Applied Mathematics, 2018)
One knows that the concept of minimality and maximality of left ideals and right ideals play an important role in semigroups. In this paper, we extend this concept to consider in n-ary semigroups. A number of results concerning relationships between minimality and maximality of n-ideals of n-ary semigroups and n-simple (0-n-simple) n-ary semigroups as well as some characterizations of minimality and maximality of n-ideals of n-ary semigroups are given.
Keywords: n-ary semigroups; i-ideals; n-ideals; minimal ideals; maximal ideals; n-simple; 0-n-simple.