Abstract
In this paper, we study the class of prime semimodules and the related concepts, such as the class of semimodules, the class of Dedekind semidomains, the class of prime semimodules which is invariant subsemimodules of its injective hull, and the compressible semimodules. In order to make the work as complete as possible, we stated, and sometimes proved, some known results related to the above concepts.
Highlights
Throughout this paper, will denote a commutative semiring with identity, and is an - semimodule.This paper consists of three sections
In Section two, we introduce the concept of density of semimodules
We use the density concept to define the class of semimodules, as is said to be semimodule if each non-zero subtractive subsemimodule of is dense in
Summary
Throughout this paper, will denote a commutative semiring with identity, and is an - semimodule. In Section one, we introduce some definitions and remarks which we will use in the paper. In Section two, we introduce the concept of density of semimodules. . We use the density concept to define the class of semimodules, as is said to be semimodule if each non-zero subtractive subsemimodule of is dense in. In Section three, we define the concept of prime semimodules, analogous to that in modules [4], where is said to be prime if ann ann( ), for each non-zero subtractive subsemimodule of. . Similar to that in modules [1], we will show that every semimodule is a prime semimodule. We generalize some types of prime modules for semimodules, such as the compressible type
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
