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| Paper IPM / M / 17598 |
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| Abstract: | |
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Let $\Gamma$ be a nonzero commutative cancellative monoid (written additively), $R = \bigoplus_{\alpha\in\Gamma}R_{\alpha}$ be a $\Gamma$-graded integral domain with $R_{\alpha} \neq \{0\}$ for all $\alpha \in \Gamma$, and $H$ be the set of nonzero homogeneous elements of $R$. A homogeneous ideal $P$ of $R$ will be said to be strongly homogeneous primary if $xy \in P$ implies $x \in P$ or $y^n\in P$ for some integer $n\geq 1$, for every homogeneous elements $x, y$ of $R_H$. We say that $R$ is a graded almost pseudo-valuation domain (gr-APVD) if each homogeneous prime ideal of $R$ is strongly homogeneous primary.
In this paper, we study some ring-theoretic properties of gr-APVDs and graded integral domains $R$ such that $R_{H\setminus P}$ is a gr-APVD for all homogeneous maximal ideals (resp., homogeneous maximal $t$-ideals) $P$ of $R$.
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