Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 63 Issue 4
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- Pages.1005-1022
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- 2026
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
DOI QR Code
HOMOGENEOUS PRIME t-IDEALS IN GRADED INTEGRAL DOMAINS
- Dong Kyu Kim (Department of Mathematics Kyungpook National University)
- Received : 2024.08.16
- Accepted : 2026.04.06
- Published : 2026.07.31
Abstract
In this paper, we define the concepts homogeneous PF-prime ideals and almost homogeneous PF-prime ideals; and study some properties of these. In detail, when R is a graded GCD-domain, we show that P is a homogeneous PF-prime ideal of R if and only if P is a homogeneous prime t-ideal of R, if and only if RH\P is a graded valuation domain. Also, when R is a graded AGCD-domain, we show that P is an almost homogeneous PF-prime ideal of R if and only if P is a homogeneous prime t-ideal of R, if and only if RH\P is a graded AV-domain.
Keywords
- Graded GCD-domain;
- homogeneous PF-prime ideal;
- homogeneous prime t-ideal;
- graded almost GCD-domain;
- almost homogeneous PF-prime ideal;
- graded almost Prufer domain;
- graded almost Bezout domain