Affiliations: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Correspondence:
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Correspondence to: T. Allahviranloo, Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. allahviranloo@yahoo.com
Abstract: In this paper, we shall embark on the study of the algebraic object known as a fuzzy ring which serves as one of the fundamental building blocks for the subject which is called fuzzy abstract algebra. The acceptable definition of fuzzy ring and field are presented with binary operations and on the basis of the specified parameter, called ambiguity rank, which fulfils the basic requirements. The properties of these fuzzy rings and their fundamental qualities are discussed. We should like to stress that these fuzzy algebraic systems and their axioms, must come from the experience of looking at many examples. Namely, they should be rich in meaningful results. Hence, the several illustrative examples are given. The future prospect of this paper is a new attitude to fuzzy basic mathematics, which will be referred to in the end.
