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Paper IPM / M / 17599  


Abstract:  
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 $H$ the saturated multiplicative set of nonzero homogeneous elements of $R$. A homogeneous prime ideal $P$ of $R$ is said to be a pseudo strongly homogeneous prime ideal if for each homogeneous elements $x, y\in R_H$ whenever $xyP\subseteq P$, then there exists a positive integer $n$, such that either $x^n \in R$ or $y^nP \subseteq P$.
A graded integral domain $R$ is said to be a graded pseudoalmost valuation domain (grPAVD) if each homogeneous prime ideal of $R$ is a pseudostrongly homogeneous prime ideal. We study the prime ideal and ringtheoretic properties and overrings of grPAVDs. We also study the grPAVD property in pullback of graded domains and give various examples of these domains.
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