Cartesian Product of Ultrasemiprime Algebras
DOI:
https://doi.org/10.29304/jqcsm.2025.17.22227Keywords:
Cartesian product, Normed algebra, Ultrasemiprime algebras, Direct product of algebrasAbstract
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.
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