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some properties of the graph of modules with respect to a first dual homomorphism
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نویسنده
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baziar m. ,zare khafri s.
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منبع
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مدل سازي پيشرفته رياضي - 2024 - دوره : 14 - شماره : 3 - صفحه:121 -129
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چکیده
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For an r-module m and f ∈ m∗ = hom(m, r), let zf(m) and regf(m) be the sets of all zero-divisors elements and regular elements of m with re- spect to f, respectively. in this paper, we introduce the total graph of m with respect to f, denoted by t(γf(m)), which is the graph with all the elements m as vertices, and for distinct elements m, n ∈ m, m and n are adjacent and only if m + n ∈ zf(m). we also study the subgraphs z(γf(m)) and reg(γf(m)) with vertices zf(m) and regf(m), respectively.
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کلیدواژه
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total graph ,zero-divisor ,regular element
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آدرس
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yasouj university, department of mathematics, iran, yasouj university, department of mathematics, iran
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پست الکترونیکی
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sa_zare66@yahoo.com
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some properties of the graph of modules with respect to a first dual homomorphism
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Authors
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Abstract
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for an r-module m and f ∈ m∗ = hom(m, r), let zf(m) and regf(m) be the sets of all zero-divisors elements and regular elements of m with re- spect to f, respectively. in this paper, we introduce the total graph of m with respect to f, denoted by t(γf(m)), which is the graph with all the elements m as vertices, and for distinct elements m, n ∈ m, m and n are adjacent and only if m + n ∈ zf(m). we also study the subgraphs z(γf(m)) and reg(γf(m)) with vertices zf(m) and regf(m), respectively.
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Keywords
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total graph ,zero-divisor ,regular element
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