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Paper IPM / M / 17599

School of Mathematics
Title:	Graded pseudo-almost valuation domains
Author(s):	Haleh Hamdi (Joint with P. Sahandi)
Status:	To Appear
Journal:	J. Algebra Appl.
Supported by:	IPM

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 pseudo-almost valuation domain (gr-PAVD) if each homogeneous prime ideal of

$R$ is a pseudo-strongly homogeneous prime ideal. We study the prime ideal- and ring-theoretic properties and overrings of gr-PAVDs. We also study the gr-PAVD property in pullback of graded domains and give various examples of these domains.

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“School of Mathematics”

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