ALGEBRAIC STRUCTURE OF THE KERNEL OF THE n-SEMINORM

Abstract

In [4], the notion of \(n\)-norm is introduced as generalization of the notion of 2-norm, introduced in [1]. In [3], the notion of \(n\)-seminorm is introduced as generalization of the notion of 2-seminorm. Equivalent definition of 2-norm is given in [2]. In the first part of this paper, we give equivalent definition of \(n\)-seminorm. In the second part of the paper, we give a characterization of the kernel of the \(n\)-seminorm as a classe of subsets of \(X^n\) and we construct two examples of 2-subspace of 2-vector space.