The Homomorphism Theorems of <i>M</i>-Hazy Rings and Their Induced Fuzzifying Convexities

Abstract

In traditional ring theory, homomorphisms play a vital role in studying the relation between two algebraic structures. Homomorphism is essential for group theory and ring theory, just as continuous functions are important for topology and rigid movements in geometry. In this article, we propose fundamental theorems of homomorphisms of M-hazy rings. We also discuss the relation between M-hazy rings and M-hazy ideals. Some important results of M-hazy ring homomorphisms are studied. In recent years, convexity theory has become a helpful mathematical tool for studying extremum problems. Finally, M-fuzzifying convex spaces are induced by M-hazy rings.

Keywords

• <i>m</i>-hazy group
• <i>m</i>-hazy ring
• <i>m</i>-hazy ideal
• <i>m</i>-hazy ring homomorphism
• <i>m</i>-fuzzifying convex space