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- W2894944320 abstract "We extend the notion of the compressed zero-divisor graph $varTheta(R)$ to noncommutative rings in a way that still induces a product preserving functor $varTheta$ from the category of finite unital rings to the category of directed graphs. For a finite field $F$, we investigate the properties of $varTheta(M_n(F))$, the graph of the matrix ring over $F$, and give a purely graph-theoretic characterization of this graph when $n neq 3$. For $n neq 2$ we prove that every graph automorphism of $varTheta(M_n(F))$ is induced by a ring automorphism of $M_n(F)$. We also show that for finite unital rings $R$ and $S$, where $S$ is semisimple and has no homomorphic image isomorphic to a field, if $varTheta(R) cong varTheta(S)$, then $R cong S$. In particular, this holds if $S=M_n(F)$ with $n neq 1$." @default.
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- W2894944320 date "2018-10-05" @default.
- W2894944320 modified "2023-10-17" @default.
- W2894944320 title "Compressed zero-divisor graphs of noncommutative rings" @default.
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