Yarı-Asal Halkalarda Ortogonal Yarı-Türevler Üzerine

Year 2016, Volume: 37 Issue: 2, 141 - 153, 06.04.2016

Öznur Gölbaşı , Fatih Bilgin

https://doi.org/10.17776/csj.45837

Abstract

Özet. Bu makalede, "  bir torsion free yarı-asal halka,  ve    örten fonksiyonu ile belirlenmiş sıfırdan farklı iki yarı-türev olmak üzere  ve   ın ortogonal olması için gerek ve yeter koşul i)  ii)  iii) her  için  iv)    fonksiyonu ile belirlenmiş bir yarı-türevdir, koşullarından herhangi birinin sağlanmasıdır" ve ayrıca "her  için i) , ii) , iii)  koşullarından birini sağlayan  halkası sıfırdan farklı bir merkezil ideal kapsar" teoremleri gösterilmiştir.

Anahtar Kelimeler: Yarı-türevler, ortogonal türevler, yarı-asal halkalar

 

Abstract. In this paper, it is shown that if  is torsion free semiprime ring,  and  are semiderivations associated with a surjective function  of ,  and  are orthogonal semiderivations if and only if the following conditions are satisfied i)  ii)  iii)   ,  iv)  is a semiderivation associated with a  function. Also, it is proved that if i) , ii) , iii)  conditions are satisfied for all  then  contains a nonzero central ideal.

Keywords: Semi-derivations, orthogonal derivations, semi-prime rings

Keywords

Yarı-türevler, ortogonal türevler, yarı-asal halkalar

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