Abstract
Abstract In a multiplication module, prime submodules have the following property: if a prime submodule contains a finite intersection of submodules, then one of the submodules is contained in the prime submodule. In this paper, we generalize this property to infinite intersection of submodules and call such prime submodules strongly prime submodules. A multiplication module in which every prime submodule is strongly prime will be called a strongly 0-dimensional module. It is also an extension of strongly 0-dimensional rings. After this we investigate properties of strongly 0-dimensional modules and give relations of von Neumann regular modules, Q -modules and strongly 0-dimensional modules
Keywords
Mathematics
Prime (order theory)
Intersection (aeronautics)
Von Neumann architecture
Multiplication (music)
Extension (predicate logic)
Pure mathematics
Associated prime
Discrete mathematics
Combinatorics
Computer science
Subject Areas
Rings, Modules, and Algebras
·Algebra and Number Theory ·Physical Sciences
Citations by Year
2015: 1
2016: 1
2017: 1
2020: 1
2022: 1
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