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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,401 - 1,407 (7page)
- DOI
- 10.4134/BKMS.b200962
이용수
초록· 키워드
오류제보하기
Let $R$ be a commutative $G$-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal $I$ of $R$ is said to be graded radically principal if $Grad(I)=Grad(\langle c\rangle)$ for some homogeneous $c\in R$, where $Grad(I)$ is the graded radical of $I$. The graded ring $R$ is said to be graded radically principal if every graded ideal of $R$ is graded radically principal. We study graded radically principal rings. We prove an analogue of the Cohen theorem, in the graded case, precisely, a graded ring is graded radically principal if and only if every graded prime ideal is graded radically principal. Finally we study the graded radically principal property for the polynomial ring $R[X]$.
목차
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참고문헌 (9)
참고문헌 신청
M. Aqalmoun / 2020 / Radically principal rings / Khayyam J. Math 6(2):243~249
W. T. Ashby / 2012 / On graded principal ideal domains / JP J. Algebra Number Theory Appl 24(2):159~171
S. E. Atani / 2007 / On the graded primary avoidance theorem / Chiang Mai J. Sci 34(2):161~164
F. Farzalipour / 2011 / On the union of graded prime submodules / Thai J. Math 9(1):49~55
R. Hazrat / 2016 / Graded rings and graded Grothendieck groups / Cambridge University Press
W. T. Ashby / 2012 / On graded principal ideal domains / JP J. Algebra Number Theory Appl 24(2):159~171
S. E. Atani / 2007 / On the graded primary avoidance theorem / Chiang Mai J. Sci 34(2):161~164
F. Farzalipour / 2011 / On the union of graded prime submodules / Thai J. Math 9(1):49~55
R. Hazrat / 2016 / Graded rings and graded Grothendieck groups / Cambridge University Press
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