Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: The original part of this thesis consists of four chapters. In the first chapter, the prime radical of an element in a (l_0)-groupoid and a prime spectrum of an (l_0)-groupoid are defined and properties of theirs are examined.In the second chapter, the theorem on prime radical of an element of an algebraic l-groupoid and its applications are given. The applications of this theorem and its corollaries are done on distributive universal algebras. In the third chapter, the intersection of the all coatoms and the sum of all atoms are defined and the relations among them are studied.In the last chapter, the integral l-groupoids of lengths 2 and 3 are described completely. In addition, in this chapter, the properties of the direct decompositions of the unit, connections between comaximal elements and direct decompositions of the unit are examined and an analog of Krull-Schmidt theorem is given in an integral l-groupoid. Key words: l-groupoid, l-monoid, semi integral l-groupoid, integral l-groupoid, prime radical, prime spectrums, atom, coatom, direct decomposition, comaximal element_: Lower indice | |||||||||||||||||||||