TRIANGULAR NORMS AND LATTICE-VALUED MODULE THEORY: ON ⊛-SUBMODULES AND ⊛-MODULE HOMOMORPHISMS
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE, cilt.16, sa.1, ss.119-129, 2026 (Hakemli Dergi)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 1
- Basım Tarihi: 2026
- Dergi Adı: BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE
- Derginin Tarandığı İndeksler: Academic Search Ultimate (EBSCO), MathSciNet, zbMATH
- Sayfa Sayıları: ss.119-129
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Recep Tayyip Erdoğan Üniversitesi Adresli: Evet
Özet
Thispaperinvestigates lattice-valued relations and functions within the framework of triangular norms (t-norms) and their applications to module theory. Building upon Demirci’s foundational work on fuzzy functions defined via fuzzy equivalence relations, we introduce and develop the concept of ⊛-module homomorphisms. Our approach extends classical module homomorphism theory to the lattice-valued setting by leveraging the structural properties of t-norms and ⊛-equivalence relations. We establish necessary preliminary concepts including t-norms, ⊛-equivalence relations, and ⊛-functions, with special attention to infinitely ∨-distributive t-norms. We then characterize ⊛-submodules and ⊛-congruence relations, proving key theorems regarding their behavior. The core contribution is the formal definition and detailed analysis of ⊛-module homomorphisms. We prove that kernels and images of ⊛-module homomorphisms are themselves ⊛-submodules, and establish fundamental homomorphism theorems in the lattice-valued context.