Properties of ϕ-Primal Graded Ideals
Author
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-06-04
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Let R be a commutative graded ring with unity 1≠0.
A proper graded ideal of R is a graded ideal I of R such that I≠R.
Let ϕ:I(R)→I(R)∪{∅} be any function, where I(R) denotes the set of all proper graded ideals of R.
A homogeneous element a∈R is ϕ-prime to I if ra∈I-ϕ(I) where r is a homogeneous element in R; then r∈I.
An element a=∑g∈Gag∈R is ϕ-prime to I if at least one component ag of a is ϕ-prime to I.
Therefore, a=∑g∈Gag∈R is not ϕ-prime to I if each component ag of a is not ϕ-prime to I.
We denote by νϕ(I) the set of all elements in R that are not ϕ-prime to I.
We define I to be ϕ-primal if the set P=νϕ(I)+ϕ(I) (if ϕ≠ϕ∅) or P=νϕ(I) (if ϕ=ϕ∅) forms a graded ideal of R.
In the work by Jaber, 2016, the author studied the generalization of primal superideals over a commutative super-ring R with unity.
In this paper we generalize the work by Jaber, 2016, to the graded case and we study more properties about this generalization.
American Psychological Association (APA)
Jaber, Ameer. 2017. Properties of ϕ-Primal Graded Ideals. Journal of Mathematics،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1182365
Modern Language Association (MLA)
Jaber, Ameer. Properties of ϕ-Primal Graded Ideals. Journal of Mathematics No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1182365
American Medical Association (AMA)
Jaber, Ameer. Properties of ϕ-Primal Graded Ideals. Journal of Mathematics. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1182365
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1182365