On 2-absorbing submodule elements in le-modules and its generalizations - ASLANKARAYİĞİT UĞURLU, EMEL (My University, 2022)
In this paper, we introduce the concept of 2-absorbing submodule elements in an le-module M as follows: a proper submodule element q in M is said to be 2-absorbing for any r,s is an element of R and m is an element of M if rsm <= q, then either rs is an element of (q : e) or rm <= q or sm <= q. Moreover, we define some generalizations of the new concept such as weakly 2-absorbing, n-absorbing, weakly n-absorbing, (n,k)-absorbing, weakly (n,k)-absorbing submodule elements in le-modules. After presenting a main example for le-modules, we study some counter examples for the generalizations. In addition to giving some characterizations for the new concepts, we investigate the relationship between prime (primary) submodule elements and them.
Keywords: Matematik; Bilgisayar Bilimleri; Fizik; Disiplinlerarası Fizik ve İlgili Bilim ve Teknoloji Alanları; Temel Bilimler; Mathematics; Computer Science; Physics; Interdisciplinary Physics and Related Science and Technology Areas; Natural Sciences; MATEMATİK, UYGULAMALI; Temel Bilimler (SCI); FİZİK, MULTİDİSİPLİNER; MATHEMATICS, APPLIED; MATHEMATICS; Natural Sciences (SCI); PHYSICS, MULTIDISCIPLINARY; PHYSICS; Analysis; Applied Mathematics; Algebra and Number Theory; Numerical Analysis; Mathematics (miscellaneous); Modeling and Simulation; General Mathematics; Computational Theory and Mathematics; Physical Sciences; complete lattices; le-modules; submodule elements; 2-absorbing (weakly 2-absorbing) submodule elements