Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58536Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)20170101Slimming and regularization of cozero maps678434407ENMohamad Mehdi EbrahimiDepartment of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran.Abolghasem Karimi FeizabadiDepartment of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.Journal Article20160527Cozero maps are generalized forms of cozero elements. Two particular cases of cozero maps, slim and regular cozero maps, are significant. In this paper we present methods to construct slim and regular cozero maps from a given cozero map. The construction of the slim and the regular cozero map from a cozero map are called slimming and regularization of the cozero map, respectively. Also, we prove that the slimming and regularization create reflector functors, and so we may say that they are the best method of constructing slim and regular cozero maps, in the sense of category theory.<br /> Finally, we give slim regularization for a cozero map $c:M\rightarrow L$ in the general case where $A$ is not a ${\Bbb Q}$-algebra. We use the ring and module of fractions, in this construction process.https://cgasa.sbu.ac.ir/article_34407_a5c130e088026ede497dc3f85308de65.pdf