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“School of Mathematics”

Paper IPM / M / 17598

School of Mathematics
Title:	Graded almost pseudo-valuation domains
Author(s):	Haleh Hamdi (Joint with P. Sahandi)
Status:	Published
Journal:	Comm. Algebra
Vol.:	52
Year:	2024
Pages:	315-326
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

$H$ 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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