English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutativering with identity and $M$ a graded $R$-module. In this paper, we introduce theconcept of graded $I_{e}$-prime submodule as a generalization of a graded primesubmodule for $I=\oplus_{g\in G}I_{g}$ a fixed graded ideal of $R$. We give anumber of results concerning of these classes of graded submodules and theirhomogeneous components. A proper graded submodule $N$ of $M$ is said to be agraded $I_{e}$-prime submodule of $M$ if whenever $% r_{g}\in h(R)$ and$m_{h}\in h(M)$ with $r_{g}m_{h}\in N-I_{e}N,$ then either $r_{g}\in (N:_{R}M)$or $m_{h}\in N.$

On graded $I_{e}$-prime submodules of graded modules over graded commutative rings