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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2020.1
- 수록면
- 1,045 - 1,056 (12page)
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초록· 키워드
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Let $R$ be a commutative ring with unity. The extension of annihilating-ideal graph of $R$, $\overline{\mathbb{AG}}(R)$, is the graph whose vertices are nonzero annihilating ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if there exist $n,m\in\mathbb{N}$ such that $I^{n}J^{m}=(0)$ with $I^{n}, J^{m}\neq (0)$. First, we differentiate when $\mathbb{AG}(R)$ and $\overline{\mathbb{AG}}(R)$ coincide. Then, we have characterized the diameter and the girth of $\overline{\mathbb{AG}}(R)$ when $R$ is a finite direct products of rings. Moreover, we show that $\overline{\mathbb{AG}}(R)$ contains a cycle, if $\overline{\mathbb{AG}}(R)\neq\mathbb{AG}(R)$.
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참고문헌 (5)
참고문헌 신청
F. Aliniaeifard / 2014 / On the Diameter and Girth of an Annihilating-Ideal Graph / arXiv: 1411.4163v1[math. RA]
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 217(2):434~447
M. Behboodi / 2011 / The annihilating-ideal graph of commutative rings I / J. Algebra Appl 10(4):727~739
M. Behboodi / 2011 / The annihilating-ideal graph of commutative rings II / J. Algebra Appl 10(4):741~753
D. Bennis / 2016 / On the extended zero divisor graph of commutative rings / Turkish J. Math 40(2):376~388
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 217(2):434~447
M. Behboodi / 2011 / The annihilating-ideal graph of commutative rings I / J. Algebra Appl 10(4):727~739
M. Behboodi / 2011 / The annihilating-ideal graph of commutative rings II / J. Algebra Appl 10(4):741~753
D. Bennis / 2016 / On the extended zero divisor graph of commutative rings / Turkish J. Math 40(2):376~388
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