Automorphisms of completely primary finite rings of characteristic p

Chiteng'a John Chikunji

Displaying similar documents to “Automorphisms of completely primary finite rings of characteristic p”

Coleman automorphisms of finite groups with a self-centralizing normal subgroup

Jinke Hai (2020)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group with a normal subgroup $N$ such that $C_{G} (N) \leq N$ . It is shown that under some conditions, Coleman automorphisms of $G$ are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.

Rings in which elements are sum of a central element and an element in the Jacobson radical

Guanglin Ma, Yao Wang, André Leroy (2024)

Czechoslovak Mathematical Journal

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An element in a ring $R$ is called CJ if it is of the form $c + j$ , where $c$ belongs to the center and $j$ is an element from the Jacobson radical. A ring $R$ is called CJ if each element of $R$ is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show...

About G-rings

Najib Mahdou (2017)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if $R \subseteq T$ is a ring extension such that $m T \subseteq R$ for some regular element $m$ of $T$ , then $T$ is a G-ring if and only if so is $R$ . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.

Rings consisting entirely of certain elements

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2018)

Czechoslovak Mathematical Journal

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We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; $ℤ_{3} \oplus ℤ_{3}$ ; $ℤ_{3} \oplus B$ where $B$ is a Boolean ring; local ring with nil Jacobson radical; $M_{2} (ℤ_{2})$ or $M_{2} (ℤ_{3})$ ; or the ring of a Morita context with zero pairings where the underlying rings are $ℤ_{2}$ or $ℤ_{3}$ .

On near-ring ideals with $(σ, τ)$ -derivation

Öznur Golbaşi, Neşet Aydin (2007)

Archivum Mathematicum

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Let $N$ be a $3$ -prime left near-ring with multiplicative center $Z$ , a $(σ, τ)$ -derivation $D$ on $N$ is defined to be an additive endomorphism satisfying the product rule $D (x y) = τ (x) D (y) + D (x) σ (y)$ for all $x, y \in N$ , where $σ$ and $τ$ are automorphisms of $N$ . A nonempty subset $U$ of $N$ will be called a semigroup right ideal (resp. semigroup left ideal) if $U N \subset U$ (resp. $N U \subset U$ ) and if $U$ is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let $D$ be a $(σ,$ $τ)$ -derivation...

A generalization of reflexive rings

Mete Burak Çalcı, Huanyin Chen, Sait Halıcıoğlu (2024)

Mathematica Bohemica

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We introduce a class of rings which is a generalization of reflexive rings and $J$ -reversible rings. Let $R$ be a ring with identity and $J (R)$ denote the Jacobson radical of $R$ . A ring $R$ is called $J$ -reflexive if for any $a, b \in R$ , $a R b = 0$ implies $b R a \subseteq J (R)$ . We give some characterizations of a $J$ -reflexive ring. We prove that some results of reflexive rings can be extended to $J$ -reflexive rings for this general setting. We conclude some relations between $J$ -reflexive rings and some related rings. We investigate some extensions...

Left EM rings

Jongwook Baeck (2024)

Czechoslovak Mathematical Journal

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Let $R [x]$ be the polynomial ring over a ring $R$ with unity. A polynomial $f (x) \in R [x]$ is referred to as a left annihilating content polynomial (left ACP) if there exist an element $r \in R$ and a polynomial $g (x) \in R [x]$ such that $f (x) = r g (x)$ and $g (x)$ is not a right zero-divisor polynomial in $R [x]$ . A ring $R$ is referred to as left EM if each polynomial $f (x) \in R [x]$ is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions....

Notes on generalizations of Bézout rings

Haitham El Alaoui, Hakima Mouanis (2021)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we give new characterizations of the $P$ - $2$ -Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non- $2$ -Bézout $P$ - $2$ -Bézout rings and examples of non- $P$ -Bézout $P$ - $2$ -Bézout rings.

Skew inverse power series rings over a ring with projective socle

Kamal Paykan (2017)

Czechoslovak Mathematical Journal

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A ring $R$ is called a right $PS$ -ring if its socle, $Soc (R_{R})$ , is projective. Nicholson and Watters have shown that if $R$ is a right $PS$ -ring, then so are the polynomial ring $R [x]$ and power series ring $R [[x]]$ . In this paper, it is proved that, under suitable conditions, if $R$ has a (flat) projective socle, then so does the skew inverse power series ring $R [[x^{- 1}; α, δ]]$ and the skew polynomial ring $R [x; α, δ]$ , where $R$ is an associative ring equipped with an automorphism $α$ and an $α$ -derivation $δ$ . Our results extend and unify many existing...

Avoidance principle and intersection property for a class of rings

Rahul Kumar, Atul Gaur (2020)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative ring with identity. If a ring $R$ is contained in an arbitrary union of rings, then $R$ is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in $R$ , then $R$ contains one of them under various conditions.

A Characterization of One-Element p-Bases of Rings of Constants

Piotr Jędrzejewicz (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in $K [x ₁^{p}, . . ., x ₙ^{p}]$ . We prove that $K [x ₁^{p}, . . ., x ₙ^{p}, f]$ is the ring of constants of a K-derivation of K[x₁,...,xₙ] if and only if all the partial derivatives of f are relatively prime. The proof is based on a generalization of Freudenburg’s lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.