Affiliation:
1. Department of Mathematics and Statistics, Jordan University of Science and Technology , Irbid , Jordan
2. Department of Mathematics, Yarmouk University , Irbid 21163 , Jordan
Abstract
Abstract
Let
G
G
be a group and
R
R
be a
G
G
-graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal. A proper graded ideal
P
P
of
R
R
is said to be a graded weakly 1-absorbing primary ideal of
R
R
if whenever nonunit elements
x
,
y
,
z
∈
h
(
R
)
x,y,z\in h\left(R)
such that
0
≠
x
y
z
∈
P
0\ne xyz\in P
, then
x
y
∈
P
xy\in P
or
z
n
∈
P
{z}^{n}\in P
, for some
n
∈
N
n\in {\mathbb{N}}
. Several properties of graded weakly 1-absorbing primary ideals are investigated.
Reference20 articles.
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3. K. Al-Zoubi, R. Abu-Dawwas, and S. Ceken, On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacettepe J. Math. Stat. 48 (2019), no. 3, 724–731.
4. F. Soheilnia and A. Y. Darani, On graded 2-absorbing and graded weakly 2-absorbing primary ideals, Kyungpook Math. J. 57 (2017), no. 4, 559–580.
5. R. Abu-Dawwas and M. Bataineh, Graded 1-absorbing primary ideals, Conference: Turkish Journal of Mathematics - Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, February 1–3, Istanbul - Turkey, 2022.
Cited by
1 articles.
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