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Research Article

Principal Ideal Rings

Ahmet Goksel Agargun
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In this paper we continue to extend ring concepts. Here we define principal ideal rings for commutative rings (not necessarily with identity) and prove that this definition is equivalent to the usual definition in the case of a ring with identity. Then we generalize some results for principal ideal rings. We study direct sums, direct summands and quotient rings. We show that every Euclidean ring is a principal ideal ring.

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  How to cite this article:

Ahmet Goksel Agargun , 2003. Principal Ideal Rings. Journal of Applied Sciences, 3: 71-75.

DOI: 10.3923/jas.2003.71.75


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