On ϕ-δ-Primary Submodules - TEKİR, ÜNSAL (My University, 2022)
In this paper, we introduce and study a new class of submodules which unify the concepts of prime and primary submodules. Let M be a unital module over a commutative ring R; / : LðMÞ ! LðMÞ[ ;f g be a reduction function and d : LðRÞ ! LðRÞ be an expansion function, where LðMÞ is the lattice of all submodules of M and LðRÞ is the lattice of all ideals of R: A proper submodule N of M is said to be a /-d-primary submodule of M if whenever am 2 N /ðNÞ for some a 2 R and m 2 M; then either a 2 dððN : MÞÞ or m 2 N: Many properties, characterizations and examples of /-d-primary submodules are given. Keywords Prime submodule Primary submodule /-Prime /-d-Primary submodule
Keywords: Matematik; Değişmeli Halkalar ve Cebirler; Temel Bilimler; Mathematics; Commutative Rings and Algebras; Natural Sciences; Temel Bilimler (SCI); Doğa Bilimleri Genel; ÇOK DİSİPLİNLİ BİLİMLER; MATEMATİK; Natural Sciences (SCI); NATURAL SCIENCES, GENERAL; MATHEMATICS; MULTIDISCIPLINARY SCIENCES; Multidisciplinary; Discrete Mathematics and Combinatorics; Geometry and Topology; Logic; Physical Sciences; Prime submodule; Primary submodule; Prime