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Graded amalgamated algebras along an ideal defined by graded 1-absorbing-like conditions.
- Source :
-
Journal of Algebra & Its Applications . Jul2024, p1. 17p. - Publication Year :
- 2024
-
Abstract
- Let G be a group with identity and R be a G-graded commutative ring with nonzero identity. A proper graded ideal I of R is called a graded 1-absorbing prime ideal (respectively, graded 1-absorbing primary ideal) if whenever nonunit homogeneous elements a,b,c ∈ R with abc ∈ I, then ab ∈ I or c ∈ I (respectively, ab ∈ I or c ∈ Gr(I), where Gr(I) is the graded radical of I). The purpose of this paper is to study the transfer of some graded 1-absorbing-like properties to the graded amalgamated algebra along an ideal (denoted by A⋈fJ). Our results provide new techniques for the construction of new original examples satisfying the above-mentioned properties. [ABSTRACT FROM AUTHOR]
- Subjects :
- *IDEALS (Algebra)
*PRIME ideals
*GROUP identity
*COMMUTATIVE rings
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 178405446
- Full Text :
- https://doi.org/10.1142/s0219498825503098