On endomorphism-regularity of zero-divisor graphs |
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| Authors: | Dancheng Lu Tongsuo Wu |
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| Institution: | a Department of Mathematics, Suzhou University, Suzhou 215006, PR China
b Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, PR China |
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| Abstract: | The paper studies the following question: Given a ring R, when does the zero-divisor graph Γ(R) have a regular endomorphism monoid? We prove if R contains at least one nontrivial idempotent, then Γ(R) has a regular endomorphism monoid if and only if R is isomorphic to one of the following rings: Z2×Z2×Z2; Z2×Z4; Z2×(Z2x]/(x2)); F1×F2, where F1,F2 are fields. In addition, we determine all positive integers n for which Γ(Zn) has the property. |
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| Keywords: | End-regular Zero-divisor graph Split graph Idempotent Local ring |
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