The Equivalence Between Ultrasemiprime and Ultraprime Under Certain Conditions

Section: Research Paper
Published
Jun 25, 2025
Pages
147-150

Abstract

Mathieu proved that any prime algebra which is also C* - algebra is an ultraprime. Brear shows that C* - algebra is an ultrasemiprime. This paper is give condtions to ultrasempirime algebras to get ultraprime. Mathieu defined ultraprime algebras by using four equivalent conditions. In his definition of ultraprime algebra, he used the ultrapower of algebra. In contrast, in other identical conditions, he once used sequences; in another occasion, he used a particular linear operator. Our proof adds a new condition by using the prime algebra to the ultrasemiprime algebra to get an equivalent condition to ultraprime algebras.

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How to Cite

Th. Al-Neima, M., رقية, N. Balo, R., نادية, & Adnan Abdalrazaq, N. (2025). The Equivalence Between Ultrasemiprime and Ultraprime Under Certain Conditions. AL-Rafidain Journal of Computer Sciences and Mathematics, 17(2), 147–150. Retrieved from https://rjps.uomosul.edu.iq/index.php/csmj/article/view/19736