Also, it is proved that if i) ?(??)=?(?)?(?), ii) ?(??)=?(?)?(?), iii) ?(??)±????conditions are satisfied for all ?,???,then ?contains a nonzero central ideal.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, it is shown that if ?is 2-torsion free semiprime ring, ?and hare semiderivations associated with a surjective function ?of ?, ?and hare orthogonal semiderivations if and only if the following conditions are satisfied i) ?h=0,ii) ?h+h?=0,iii) ????, ?(?)h(?)=0,iv) ?his a semiderivation associated with a ?2function.
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Key Findings & Data:In this paper, it is shown that if ?is 2-torsion free semiprime ring, ?and hare semiderivations associated with a surjective function ?of ?, ?and hare orthogonal semiderivations if and only if the following conditions are satisfied i) ?h=0,ii) ?h+h?=0,iii) ????, ?(?)h(?)=0,iv) ?his a semiderivation associated with a ?2function.
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Conclusion & Impact:Also, it is proved that if i) ?(??)=?(?)?(?), ii) ?(??)=?(?)?(?), iii) ?(??)±????conditions are satisfied for all ?,???,then ?contains a nonzero central ideal.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, it is shown that if ?is 2-torsion free semiprime ring, ?and hare semiderivations associated with a surjective function ?of ?, ?and hare orthogonal semiderivations if and only if the following conditions are satisfied i) ?h=0,ii) ?h+h?=0,iii) ????, ?(?)h(?)=0,iv) ?his a semiderivation associated with a ?2function. Also, it is proved that if i) ?(??)=?(?)?(?), ii) ?(??)=?(?)?(?), iii) ?(??)±????conditions are satisfied for all ?,???,then ?contains a nonzero central ideal.
Özet
Bu makalede, "?bir 2-torsion free yarı-asal halka, ?ve h,?örten fonksiyonu ile belirlenmiş sıfırdan farklıiki yarı-türev olmak üzere ?ve hın ortogonal olmasıiçin gerek ve yeter koşuli) ?h=0,ii) ?h+h?=0,iii) her ???için ?(?)h(?)=0,iv) ?h,?2fonksiyonu ile belirlenmiş bir yarı-türevdir, koşullarındanherhangi birinin sağlanmasıdır" ve ayrıca "her ?,???için i) ?(??)=?(?)?(?), ii) ?(??)=?(?)?(?), iii) ?(??)±????koşullarından birini sağlayan?halkası sıfırdan farklıbir merkezil ideal kapsar" teoremleri gösterilmiştir.
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Cite This Article
GÖLBAŞI, Ö., BİLGİN, F. (2022). On The Orthogonal Semi Derivatives in Semi Principal Rings. Cumhuriyet Üniversitesi Fen-Edebiyat Fakültesi Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 2, 141–153. https://ajindex.com/articles/480431
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