Cartesian Product of Ultrasemiprime Algebras

Abstract

proven to be ultrasemiprime algebras using the max norm. Since all norms are equivalent in finite dimensions, normed finite-dimensional algebras will be ultrasemiprime under any norm. However, is this true for infinite-dimensional algebras? A study addressed the direct sum of ultrasemiprime algebras using the max​ norm and another considered the sum of norms. In this research, we proved that the direct sum of ultrasemiprime algebras is ultrasemiprime under different norms.