Slimming and regularization of cozero maps

• Main Authors: Mohamad Mehdi Ebrahimi, Abolghasem Karimi Feizabadi
• Format: Article
• Language: English
• Published: Shahid Beheshti University 2017-01-01
• Series: Categories and General Algebraic Structures with Applications
• Subjects: Frame; cozero map; slim; slimming; algebraic; regular; regularization
• Online Access: http://www.cgasa.ir/article_34407_a5c130e088026ede497dc3f85308de65.pdf

Cozero 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. Finally, we give slim regularizationfor a cozero map $c:Mrightarrow L$ in the general case where $A$is not a ${Bbb Q}$-algebra. We use the ring and module offractions, in this construction process.