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In this book we introduce the concepts of (the completely semi prime ideal, Smarandache completely semi prime ideal) with respect to an element of a near ring in fuzzy and ordinary senses. We explain these concepts with some examples and we prove some propositions and theorems about it. Also, we give the relationships among these types and other types of ideals. These types of ideals depend on specific element of a near ring.

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Prof. Husein Hadi Abbass is Dean´s assistant for scientific affairs - Faculty of computer science and maths -Kufa university. He has 50 researches published in local and international magazines in the fields of algebra, applied mathematics, image processing, genetic algorithms, fuzzy math´s and (5) books in algebra.

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