Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a $G$-graded commutative ring with a nonzero unity and $P$ be a proper graded ideal of $R$. Then $P$ is said to be a graded uniformly $pr$-ideal of $R$ if there exists $n\in \mathbb{N}$ such that whenever $a, b\in h(R)$ with $ab\in P$ and $Ann(a)=\{0\}$, then $b^{n}\in P$. The smallest such $n$ is called the order of $P$ and is denoted by $ord_{R}(P)$. In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly $pr$-ideals in graded factor rings and in direct product of graded rings.

Keywords: Graded $r$-ideals, graded $pr$-ideals, graded uniformly $pr$-ideals

MSC numbers: Primary 13A02, 16W50