Graded ? -2-Absorbing and Graded ? -2-Absorbing Primary Submodules

Azzh Saad Alshehry, Malik Bataineh and Rashid Abu-Dawwas
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Azzh Saad Alshehry: Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Malik Bataineh: Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan
Rashid Abu-Dawwas: Department of Mathematics, Yarmouk University, Irbid 21163, Jordan

Mathematics, 2021, vol. 9, issue 10, 1-10

Abstract: The main goal of this article is to explore the concepts of graded ? -2-absorbing and graded ? -2-absorbing primary submodules as a new generalization of the concepts of graded 2-absorbing and graded 2-absorbing primary submodules. Let ? : G S ( M ) ? G S ( M ) ? { ? } be a function, where G S ( M ) denotes the collection of graded R -submodules of M . A proper K ? G S ( M ) is said to be a graded ? -2-absorbing R -submodule of M if whenever x , y are homogeneous elements of R and s is a homogeneous element of M with x y s ? K ? ? ( K ) , then x s ? K or y s ? K or x y ? ( K : R M ) , and we call K a graded ? -2-absorbing primary R -submodule of M if whenever x , y are homogeneous elements of R and s is a homogeneous element of M with x y s ? K ? ? ( K ) , then x s or y s is in the graded radical of K or x y ? ( K : R M ) . Several properties of these new forms of graded submodules are investigated.

Keywords: graded primary submodules; graded 2-absorbing submodules; graded 2-absorbing primary submodules (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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