The commutativity in prime Gamma rings with left derivation
نویسندگان
چکیده
منابع مشابه
Some commutativity theorems for $*$-prime rings with $(sigma,tau)$-derivation
Let $R$ be a $*$-prime ring with center $Z(R)$, $d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated automorphisms $sigma$ and $tau$ of $R$, such that $sigma$, $tau$ and $d$ commute with $'*'$. Suppose that $U$ is an ideal of $R$ such that $U^*=U$, and $C_{sigma,tau}={cin R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper, it is shown that if charac...
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let $r$ be a $*$-prime ring with center $z(r)$, $d$ a non-zero $(sigma,tau)$-derivation of $r$ with associated automorphisms $sigma$ and $tau$ of $r$, such that $sigma$, $tau$ and $d$ commute with $'*'$. suppose that $u$ is an ideal of $r$ such that $u^*=u$, and $c_{sigma,tau}={cin r~|~csigma(x)=tau(x)c~mbox{for~all}~xin r}.$ in the present paper, it is shown that...
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Let N be a prime Γ-near ring with multiplicative center Z. Let σ and τ be automorphisms of N and δ be a Γ− (σ, τ)-derivation of N such that N is 2-torsion free. In this paper the following results are proved: (1) If σγδ = δγσ and τγδ = δγτ and δ(N) ⊆ Z, or [δ(x), δ(y)]γ = 0, for all x, y ∈ N and γ ∈ Γ, then N is a commutative ring. (2) If δ1 is a Γ-derivation, δ2 is a Γ − (σ, τ) derivation of N...
متن کاملTwo Torsion Free Prime Gamma Rings With Jordan Left Derivations
Let M be a 2-torsion free prime Γ-ring and X a nonzero faithful and prime ΓM -module. Then the existence of a nonzero Jordan left derivation d : M → X satisfying some appropriate conditions implies M is commutative. M is also commutative in the case that d : M → M is a derivation along with some suitable assumptions. AMS (MOS) Subject Classification Codes: 03E72, 54A40, 54B15
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ژورنال
عنوان ژورنال: International Mathematical Forum
سال: 2007
ISSN: 1314-7536
DOI: 10.12988/imf.2007.07008