منابع مشابه
Rigid left Noetherian rings
Let R be an associative ring. A map σ : R → R is called a ring endomorphism if σ(x+y) = σ(x)+σ(y) and σ(xy) = σ(x)σ(y) for all elements a,b ∈ R. A ring R is said to be rigid if it has only the trivial ring endomorphisms, that is, identity idR and zero 0R . Rigid left Artinian rings were described by Maxson [9] and McLean [11]. Friger [4, 6] has constructed an example of a noncommutative rigid r...
متن کاملOre Extensions over Weak Σ - Rigid Rings
Let R be a ring, σ an automorphism of R and δ a σ-derivation of R. We recall that a ring R is said to be a δ-ring if aδ(a) ∈ P (R) implies a ∈ P (R), where P (R) denotes the prime radical of R. It is known that, if R is a Noetherian ring, σ an automorphism of R such that aσ(a) ∈ P (R) implies a ∈ P (R) and δ a σ-derivation of R such that R is a δ-ring with σ(δ(a)) = δ(σ(a)), for all a ∈ R, then...
متن کاملArtemovych O.d., Lukashenko M.p. on Rigid Derivations in Rings
We prove that in a ring Rwith an identity there exists an element a ∈ R and a nonzero derivation d ∈ Der R such that ad(a) 6= 0. A ring R is said to be a d-rigid ring for some derivation d ∈ Der R if d(a) = 0 or ad(a) 6= 0 for all a ∈ R. We study rings with rigid derivations and establish that a commutative Artinian ring R either has a non-rigid derivation or R = R1 ⊕ · · · ⊕ Rn is a ring direc...
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BACKGROUND Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or fle...
متن کاملHighly deformable actuators made of dielectric elastomers clamped by rigid rings
by rigid rings Tongqing Lu, Choon Chiang Foo, Jiangshui Huang, Jian Zhu, and Zhigang Suo State Key Lab for Strength and Vibration of Mechanical Structures, International Center for Applied Mechanics, School of Aerospace Engineering, Xi’an Jiaotong University, 710049 Xi’an, China School of Engineering and Applied Sciences, Kavli Institute for Nanobio Science and Technology, Harvard University, C...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1978
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500016059