Symmetric Higher Bi-Left (Right)Centerlizerhomo of Γ Ring - Lubna Abdullah Khayoon Lazim; Salah Mahdi Salah (International Journal of Scientific Research in Science, Engineering and Technology, 2025)
This chapter investigates the structural properties of symmetric higher bi-left (right) centerlizerhomomorphisms (SHBL(r.r)CH) within the framework of Γ-rings. In the first section, the notions of SHBL(r.r)CH, jointly symmetric higher bi-left (right) centerlizerhomomorphisms (JSHBL(r.r)CH), and jointly totally symmetric higher bi-left (right) centerlizerhomomorphisms (JTSHBL(r.r)CH) are introduced and rigorously examined. The interrelations among these mappings are explored in depth, leading to the significant result that every SHBL(r.r)CH of a Γ-ring is also a JTSHBL(r.r)CH. The second section of the chapter generalizes these findings to broader classes of Γ-rings, providing a unified framework for future research in this area. These developments contribute to a deeper understanding of homomorphic mappings in Γ-ring theory and their symmetric structures.
Keywords: Γ-ring; symmetric higher bi-left (right) centerlizerhomomorphism (SHBL(r.r)CH); jointly symmetric higher bi-left (right) centerlizerhomomorphism (JSHBL(r.r)CH); jointly totally symmetric higher bi-left (right) centerlizerhomomorphism (JTSHBL(r.r)CH); homomorphism; ring theory; structure-preserving maps; generalization