TY - JOUR ID - 144158 TI - On graded strongly $1$-absorbing primary ideals JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Abu-Dawwas, Rashid AD - Department of Mathematics, Yarmouk University, Irbid, Jordan Y1 - 2022 PY - 2022 VL - 8 IS - 1 SP - 42 EP - 52 KW - Graded prime ideal KW - Graded absorbing ideal KW - Graded primary ideal DO - 10.22034/kjm.2021.265610.2121 N2 - Let $G$ be a group with identity $e$ and $R$ be a $G$-graded commutative ring with nonzero unity $1$. In this article, we introduce the concept of graded strongly $1$-absorbing primary ideals. A proper graded ideal $P$ of $R$ is said to be a graded strongly $1$-absorbing primary ideal of $R$ if whenever nonunit homogeneous elements $x, y, z\in R$ such that $xyz\in P$, then either $xy\in P$ or $z\in Grad(\{0\})$ (the graded radical of $\{0\}$). Several properties of graded strongly $1$-absorbing primary ideals are investigated. Many results are given to disclose the relations between this new concept and others that already exist. Namely, the graded prime ideals, the graded primary ideals, and the graded $1$-absorbing primary ideals. UR - https://www.kjm-math.org/article_144158.html L1 - https://www.kjm-math.org/article_144158_2fb2ce58559d3c9ee576f023a2a774b6.pdf ER -