Results 81 to 90 of about 263 (93)

Perfect essential graphs [PDF]

, 2019
Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. Let EG(R) be a simple undirect graph associated with R whose vertex set is the set of all nonzero zero-divisors of R and and two distinct vertices x,
Azadi, Abdolreza, Nikmehr, M. Javad, Soleymanzadeh, B.   +2 more
core   +1 more source

A note on $σ$-reversibility and $σ$-symmetry of skew power series rings [PDF]

International Journal of Algebra, Vol. 3, 2009, no. 9, 435 - 442, 2009
Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we study the transfert of the symmetry ($\sigma$-symmetry) and reversibility ($\sigma$-reversibility) from $R$ to its skew power series ring $R[[x;\sigma]]$. Moreover, we study on the relationship between the Baerness, quasi-Baerness and p.p.-property of a ring $R$ and these of the ...
arxiv  

Commutativity conditions on derivations and Lie ideals $σ$-prime rings [PDF]

arXiv, 2009
Let $R$ be a 2-torsion free $\sigma$-prime ring, $U$ a nonzero square closed $\sigma$-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d = 0$ or $U \subseteq Z(R)$. 2) If either $d([x, y]) = 0$ for all $x, y \in U$, or $[d(x), d(y)] = 0$ for all $x, y \in U$ and $d ...
arxiv  

A constructive counterpart of the subdirect representation theorem for reduced rings [PDF]

arXiv
We give a constructive counterpart of the theorem of Andrunakievi\v{c} and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying $\forall x\in A. x^3=x$ is commutative from a classical proof.
arxiv  

Positive spoof Lehmer factorizations [PDF]

arXiv
We investigate the integer solutions of Diophantine equations related to Lehmer's totient conjecture. We give an algorithm that computes all nontrivial positive spoof Lehmer factorizations with a fixed number of bases $r$, and enumerate all nontrivial positive spoof Lehmer factorizations with 6 or fewer factors.
arxiv  

An identity with derivations in prime rings [PDF]

, 2018
Shuliang, Huang
core   +1 more source

Certain polynomial identities and commutativity of rings [PDF]

, 2000
Ashraf, Mohammad
core  

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On Centralizing Automorphisms and Jordan Left Derivations on sigma-Prime Gamma Rings

, 2015
Let M be a 2-torsion free -prime -ring and U be a non-zero -square closed Lie ideal of M. If T : M ! M is an automorphism on U such that T 6 1 and T = T on U, then we prove that U Z(M). We also study the additive maps d : M! M such that d(uu ) = 2ud (u),
K. Dey, A. C. Paul, B. Davvaz
semanticscholar   +1 more source

Results on multiplicative semiderivations in semiprime rings

, 2018
Let R be a semiprime ring. An additive mapping d : R→ R is called a semiderivation if there exists a function g : R → R such that (i) d(xy) = d(x)g(y) + xd(y) = d(x)y + g(x)d(y) and (ii) d(g(x)) = g(d(x)) hold for all x, y ∈ R.
Onur Agirtici, Ö. Gölbasi
semanticscholar   +1 more source

On Gamma-derivations in the projective product of gamma rings

, 2015
This paper highlights many enlightening results on various Gamma-derivations in the projective product of Gamma-rings. If (X,  ) is the projective product of two Gamma-rings ( X1, 1  ) and ( X2 , 2  ), a pair of derivations D1 and D2 on ( X1, 1 ...
Ranu Paul
semanticscholar   +1 more source