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perfectness of the annihilator graph of artinian commutative rings
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نویسنده
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adlifard m. ,payrovi sh.
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منبع
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journal of algebraic systems - 2023 - دوره : 10 - شماره : 2 - صفحه:335 -343
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چکیده
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let r be a commutative ring and z(r) be the set ofits zero-divisors. the annihilator graph of r, denoted by ag(r) is a simple undirected graph whose vertex set is z(r) ∗ , the set of all nonzero zero-divisors of r, and two distinct vertices x and y are adjacent if and only if annr(xy) ̸= annr(x) ∪ annr(y). in this paper, perfectness of the annihilator graph for some classes of rings is investigated. more precisely, we show that if r is an artinian ring, then ag(r) is perfect.
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کلیدواژه
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artinian ring، annihilator graph، perfectness
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آدرس
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islamic azad university, roudbar branch, department of mathematics, iran, imam khomeini international university, department of mathematics, iran
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پست الکترونیکی
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shpayrovi@sci.ikiu.ac.ir
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Authors
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