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On Nilary Group Rings
Al-Mallah, Omar A....

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On Nilary Group Rings by Al-Mallah, Omar A. ( Author )
Lemonjar Open Access
N.A
11-12-2014
In a ring A an ideal I is called (principally) nilary if for any two (principal) ideals V,W in A with VW⊆I, then either Vn⊆I or Wm⊆I, for some positive integers m and n depending on V and W; a ring A is called (principally) nilary if the zero ideal is a (principally) nilary ideal~\cite{Birkenmeier2013133}. Let G be a group and A be a ring with unity. It is natural to ask when the group ring A[G] is a (principally) nilary ring. We proved that, if A[G] is a (principally) nilary ring, then the ring A is a (principally) nilary ring; also, we proved that if A[G] is a (principally) nilary ring and G is a torsion group, then A is a (principally) nilary ring and G is a p-group and p is nilpotent in A; the converse, let G be an abelian or locally finite group, if A is a principally nilary ring and G is a p-group and p is nilpotent in A then A[G] is a principally nilary ring. Also, for a finite group G, we proved that, A[G] is a (principally) nilary ring iff A is a (principally) nilary ring and G is a p-group and p is nilpotent in A. Finally, we show that if F is a field of prime characteristic p and G is a finite (abelian or locally finite) p-group, then the group algebra F[G] is a (principally) nilary ring.
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Article
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36.88 KB
English
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MYR 0.01
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http://arxiv.org/abs/1412.3571
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