Graded coprime submodules
TL;DR: In this article, some properties of graded coprime submodules are discussed, and it is shown that if M is a generated finite generated module, then two graded submodules N and K of M are grade-coprime if and only if gradM(N) and gradM (K) are graded coprocessor submodules.
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Abstract: Let G be a group. Let R be a G-graded commutative ring with identity, and let M be a G-graded module over R .T wo graded submodules N and K of graded module M are called graded coprime whenever N + K = M .I n this paper, some properties of graded coprime submodules are discussed. For example, we show that if M is ag raded fi nitely generated module, then two graded submodules N and K of M are graded coprime if and only if gradM(N) and gradM(K) are graded coprime.
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Citations
On graded quasi-primary submodules of graded modules over graded commutative rings
Khaldoun Al-Zoubi,Rweili Alkhalaf +1 more
- 01 Jan 2021
TL;DR: In this article, the authors introduce the concept of graded quasi-primary submodules of graded modules over graded commutative rings, and consider various properties of these submodules, e.g., the properties of a given submodal group with identity.
ON GRADED (m, N)-Closed SUBMODULES
Rezvan Varmazyar
TL;DR: This paper explores graded (m, n)-closed submodules of graded A-modules, generalizing graded (m, n)-closed ideals, and investigates GC(n)(m)-rad property, providing basic properties and characterizations of these submodules in G-graded commutative rings.
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