On graded 1-absorbing primary ideals and graded
weakly 1-absorbing primary ideals
Mohammed Issoual\,^1 and Emel Aslankarayigit Ugurlu\,^2
\,^{1} CRMEF Fès, Morocco.
\,^{2} Department of Mathematics, Marmara University, Istanbul, Turkey.
Pages 152-167 | Received 20 June 2024, Accepted 20 January 2025, Published 26 January 2026
Abstract
Let G be a group with identity e and R a G-graded commutative ring with (1 \neq 0 ). In this paper, we study the concepts of graded 1-absorbing primary and graded weakly 1-absorbing primary ideals within G-graded rings. We aim to compare them with other ideal types, such as graded primary (graded weakly primary) and graded 2-absorbing primary (graded weakly 2-absorbing primary). Additionally, we examine their primary properties and investigate their behavior under G-graded ring homomorphisms. We also provide characterizations of these classes of ideals in contexts such as localizations of graded rings, graded trivial ring extensions, and graded amalgamation algebras along an ideal.
Keywords: Graded ring, graded ideal, graded 1-absorbing primary ideal, graded weakly 1-absorbing primary, graded primary ideal, graded prime ideal, trivial ring extension, graded module, graded submodule.
MSC numbers: 13A15, 13A02, 13C05, 13H05.
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