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Isomorphic digraphs from powers modulo $p$

Guixin Deng; Pingzhi Yuan — 2011

Czechoslovak Mathematical Journal

Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of vertices is ${1, 2, ..., p - 1}$ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^{k} \equiv b (mod p)$ . In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}} ≃ G_{p}^{k_{2}}$ .

On the binary system of factors of formal matrix rings

Weining Chen; Guixin Deng; Huadong Su — 2020

Czechoslovak Mathematical Journal

We investigate the formal matrix ring over $R$ defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.

Nil-clean and unit-regular elements in certain subrings of $𝕄_{2} (ℤ)$

Yansheng Wu; Gaohua Tang; Guixin Deng; Yiqiang Zhou — 2019

Czechoslovak Mathematical Journal

An element in a ring is clean (or, unit-regular) if it is the sum (or, the product) of an idempotent and a unit, and is nil-clean if it is the sum of an idempotent and a nilpotent. Firstly, we show that Jacobson’s lemma does not hold for nil-clean elements in a ring, answering a question posed by Koşan, Wang and Zhou (2016). Secondly, we present new counter-examples to Diesl’s question whether a nil-clean element is clean in a ring. Lastly, we give new examples of unit-regular elements that are...

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Currently displaying 1 – 3 of 3

Isomorphic digraphs from powers modulo $p$

On the binary system of factors of formal matrix rings

Nil-clean and unit-regular elements in certain subrings of $𝕄_{2} (ℤ)$

Advanced Search

Formula preview

Currently displaying 1 – 3 of 3

Isomorphic digraphs from powers modulo p

On the binary system of factors of formal matrix rings

Nil-clean and unit-regular elements in certain subrings of 𝕄 2 ( ℤ )

Isomorphic digraphs from powers modulo $p$

Nil-clean and unit-regular elements in certain subrings of $𝕄_{2} (ℤ)$