The Equivalence Between Ultrasemiprime and Ultraprime Under Certain Conditions | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Volume 17, Issue 2, December 2023, Pages 147-150 PDF (331.19 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2023.143922.1090 | ||
| Authors | ||
| Mohammed Al-Neima* 1; Ruqayah N. Balo2; Nadia Adnan Abdalrazaq3 | ||
| 1Civil Engineering, College of Engineering, Mosul, Iraq | ||
| 2جامعة الموصل كلية التربية للعلوم الصرفة | ||
| 3جامعة الموصل كلية التربية للعلوم الصرفة | ||
| Abstract | ||
| Mathieu proved that any prime algebra which is also C* - algebra is an ultraprime. Brešar 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. | ||
| Keywords | ||
| ultraprime algebra; ultrasemiprime algebra; ultrapower algebra | ||
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