The Journal of the Indian Mathematical Society

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On Fully Ordered Rings


     

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In this paper, we localize a fully ordered ring suitably and show that fully ordered noetberian rings are embedded order isomorphically into fully ordered local rings. We define o-local rings as a special class of fully ordered local rings and we prove for a special subclass of o-local rings a structure theorem (Theorem 3.7) similar to the structure of complete local rings.
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  • On Fully Ordered Rings

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Abstract


In this paper, we localize a fully ordered ring suitably and show that fully ordered noetberian rings are embedded order isomorphically into fully ordered local rings. We define o-local rings as a special class of fully ordered local rings and we prove for a special subclass of o-local rings a structure theorem (Theorem 3.7) similar to the structure of complete local rings.